| Preface |
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xxiii | |
| Acknowledgments |
|
xxix | |
| About the Author |
|
xxxi | |
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|
xxxiii | |
| Notations and Symbols |
|
xxxvii | |
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Introduction and Overview |
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1 | (16) |
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Linear and Numerical Linear Algebra (Chapter 2 and Chapters 3 and 4) |
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2 | (1) |
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System Responses (Chapter 5) |
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3 | (1) |
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Controllability and Observability problems (Chapter 6) |
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4 | (1) |
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Stability and Inertia (Chapter 7) |
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5 | (1) |
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Lyapunov, Sylvester, and Algebraic Riccati Equations (Chapters 8 and 13) |
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6 | (2) |
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Realization and Identification (Chapter 9) |
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8 | (1) |
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Feedback Stabilization and Eigenvalue Assignment (Chapters 10 and 11) |
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9 | (1) |
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State Estimation (Chapter 12) |
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10 | (1) |
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Internal Balancing and Model Reduction (Chapter 14) |
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11 | (1) |
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Nearness to Uncontrollability and Instability (Chapters 6 and 7) and Robust Stability and Stability Radius (Chapters 7 and 10) |
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12 | (1) |
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Nearness to Uncontrollability and Instability |
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12 | (1) |
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Robust Stability and Stability Radius (Chapters 7 and 10) |
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13 | (1) |
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Sensitivity and Condition Numbers of Control Problems |
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13 | (1) |
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14 | (1) |
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Software for Control Problems |
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15 | (2) |
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15 | (2) |
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PART I REVIEW OF LINEAR AND NUMERICAL LINEAR ALGEBRA |
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17 | (88) |
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A Review of Some Basic Concepts and Results from Theoretical Linear Algebra |
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19 | (14) |
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19 | (1) |
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Orthogonality of Vectors and Subspaces |
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19 | (1) |
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20 | (3) |
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The Characteristic Polynomial, the Eigenvalues, and the Eigenvectors of a Matrix |
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20 | (1) |
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21 | (1) |
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21 | (1) |
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22 | (1) |
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The Generalized Inverse of a Matrix |
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22 | (1) |
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22 | (1) |
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22 | (1) |
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23 | (4) |
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Diagonal and Triangular Matrices |
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23 | (1) |
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Unitary (Orthogonal) Matrix |
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23 | (1) |
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24 | (1) |
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Hessenberg (Almost Triangular) Matrix |
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24 | (1) |
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25 | (1) |
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25 | (1) |
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The Jordan Canonical Form of a Matrix |
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25 | (1) |
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26 | (1) |
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26 | (1) |
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27 | (3) |
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27 | (1) |
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28 | (2) |
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Norm Invariant Properties Under Unitary Matrix Multiplication |
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30 | (1) |
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Kronecker Product, Kronecker Sum, and Vec Operation |
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31 | (1) |
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Chapter Notes and Further Reading |
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31 | (2) |
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32 | (1) |
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Some Fundamental Tools and Concepts from Numerical Linear Algebra |
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33 | (46) |
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33 | (1) |
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Floating Point Numbers and Errors in Computations |
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34 | (3) |
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34 | (1) |
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35 | (1) |
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Laws of Floating Point Arithmetic |
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36 | (1) |
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Catastrophic Cancellation |
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37 | (1) |
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Conditioning, Efficiency, Stability, and Accuracy |
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37 | (8) |
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Algorithms and Pseudocodes |
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37 | (1) |
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Solving an Upper Triangular System |
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37 | (1) |
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Solving a Lower Triangular System |
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38 | (1) |
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Efficiency of an Algorithm |
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38 | (1) |
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The Concept of Numerical Stability |
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39 | (1) |
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Conditioning of the Problem and Perturbation Analysis |
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40 | (1) |
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Conditioning of the Problem, Stability of the Algorithm, and Accuracy of the Solution |
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41 | (1) |
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Conditioning of the Linear System and Eigenvalue Problems |
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42 | (3) |
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45 | (8) |
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LU Factorization using Gaussian Elimination |
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45 | (6) |
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The Cholesky Factorization |
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51 | (1) |
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LU Factorization of an Upper Hessenberg Matrix |
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52 | (1) |
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Numerical Solution of the Linear System Ax = b |
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53 | (3) |
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Solving Ax = b using the Inverse of A |
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53 | (1) |
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Solving Ax = b using Gaussian Elimination with Partial Pivoting |
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53 | (2) |
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Solving a Hessenberg Linear System |
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55 | (1) |
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55 | (1) |
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56 | (1) |
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Computing the Determinant of A |
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56 | (1) |
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56 | (1) |
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56 | (7) |
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57 | (1) |
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The Householder QR Factorization |
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58 | (2) |
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60 | (2) |
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The QR Factorization Using Givens Rotations |
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62 | (1) |
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The QR Factorization of a Hessenberg Matrix Using Givens Matrices |
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63 | (1) |
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Orthonormal Bases and Orthogonal Projections Using QR Factorization |
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63 | (1) |
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The Least-Squares Problem |
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64 | (3) |
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Solving the Least-Squares Problem Using Normal Equations |
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65 | (1) |
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Solving the Least-Squares Problem Using QR Factorization |
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65 | (2) |
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The Singular Value Decomposition (SVD) |
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67 | (8) |
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The Singular Value Decomposition and the Structure of a Matrix |
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68 | (1) |
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Orthonormal Bases and Orthogonal Projections |
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69 | (1) |
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The Rank and the Rank-Deficiency of a Matrix |
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70 | (2) |
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72 | (1) |
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Solving the Least-Squares Problem Using the Singular Value Decomposition |
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72 | (3) |
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75 | (3) |
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Chapter Notes and Further Reading |
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78 | (1) |
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78 | (1) |
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Canonical forms Obtained Via Orthogonal Transformations |
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79 | (26) |
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Importance and Significance of Using Orthogonal Transformations |
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79 | (2) |
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Hessenberg Reduction of a Matrix |
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81 | (2) |
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Uniqueness in Hessenberg Reduction: The Implicit Q Theorem |
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82 | (1) |
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The Real Schur Form of A: The QR Iteration Method |
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83 | (8) |
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84 | (1) |
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The Hessenberg QR Iteration and Shift of Origin |
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85 | (1) |
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The Double Shift QR Iteration |
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85 | (1) |
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Obtaining the Real Schur Form A |
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86 | (2) |
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The Real Schur Form and Invariant Subspaces |
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88 | (2) |
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90 | (1) |
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Computing the Singular Value Decomposition (SVD) |
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91 | (3) |
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The Generalized Real Schur Form: The QZ algorithm |
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94 | (5) |
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Reduction to Hessenberg-Triangular Form |
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95 | (3) |
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Reduction to the Generalized Real Schur Form |
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98 | (1) |
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Computing of the Eigenvectors of the Pencil A -- λ B |
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99 | (2) |
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101 | (1) |
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Chapter Notes and Further Reading |
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102 | (3) |
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103 | (2) |
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PART II CONTROL SYSTEMS ANALYSIS |
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105 | (200) |
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Linear State-Space Models and Solutions of the State Equations |
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107 | (52) |
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107 | (1) |
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State-Space Representations of Control Systems |
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108 | (14) |
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108 | (11) |
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119 | (1) |
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119 | (3) |
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Solutions of a Continuous-Time System: System Responses |
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122 | (17) |
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Some Important Properties of the Matrix eAt |
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126 | (1) |
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127 | (1) |
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Computational Methods for eAt |
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128 | (9) |
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Comparison of Different Methods for Computing the Exponential Matrix |
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137 | (1) |
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Evaluating an Integral with the Exponential Matrix |
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137 | (2) |
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State-Space Solution of the Discrete-Time System |
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139 | (1) |
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Transfer Function and Frequency Response |
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140 | (6) |
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140 | (2) |
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The Frequency Response Matrix and its Computation |
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142 | (4) |
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146 | (3) |
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Matlab Control System Toolbox |
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146 | (1) |
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147 | (1) |
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147 | (1) |
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148 | (1) |
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149 | (2) |
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Chapter Notes and Further Reading |
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151 | (8) |
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151 | (5) |
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156 | (3) |
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Controllability, Observability, and Distance to Uncontrollability |
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159 | (42) |
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159 | (1) |
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Controllability: Definitions and Basic Results |
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160 | (5) |
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Controllability of a Continuous-Time System |
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160 | (4) |
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Controllability of a Discrete-Time System |
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164 | (1) |
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Observability: Definitions and Basic Results |
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165 | (2) |
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Observability of a Continuous-Time System |
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165 | (2) |
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Observability of a Discrete-Time System |
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167 | (1) |
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Decompositions of Uncontrollable and Unobservable Systems |
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167 | (2) |
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Controller- and Observer-Canonical Forms |
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169 | (2) |
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Numerical Difficulties with theoretical criteria of controllability and observability |
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171 | (2) |
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A Numerically Effective Test of Controllability |
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173 | (10) |
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A Numerically Effective Test of Observability |
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183 | (1) |
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Distance to an Uncontrollable System |
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183 | (7) |
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Newton's and the Bisection Methods for Computing the Distance to Uncontrollability |
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185 | (3) |
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The Wicks--DeCarlo Method for Distance to Uncontrollability |
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188 | (2) |
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A Global Minimum Search Algorithm |
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190 | (1) |
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Distance to Uncontrollability and the Singular values of the Controllability Matrix |
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190 | (2) |
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192 | (1) |
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Matlab Control System Toolbox |
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192 | (1) |
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192 | (1) |
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192 | (1) |
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193 | (1) |
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193 | (1) |
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193 | (1) |
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Chapter Notes and Further Reading |
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194 | (7) |
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194 | (4) |
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198 | (3) |
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Stability, Inertia, and Robust Stability |
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201 | (44) |
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201 | (1) |
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Stability of a Continuous-time System |
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202 | (11) |
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Eigenvalue Criterion of Continuous-Time Stability |
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203 | (2) |
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Continuous-Time Lyapunov Stability Theory |
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205 | (5) |
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Lyapunov Equations and Controllability and Observability Grammians |
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210 | (1) |
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Lyapunov Equations and the H2-Norm |
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211 | (2) |
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Stability of a Discrete-time System |
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213 | (2) |
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Stability of a Homogeneous Discrete-Time System |
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213 | (2) |
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215 | (3) |
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The Sylvester Law of Inertia |
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216 | (1) |
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The Lyapunov Inertia Theorems |
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217 | (1) |
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Determining the Stability and Inertia of a Nonsymmetric Matrix |
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218 | (5) |
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Distance to an Unstable System |
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223 | (7) |
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230 | (2) |
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The Structured Stability Radius |
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232 | (3) |
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235 | (1) |
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Matlab Control System Toolbox |
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235 | (1) |
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235 | (1) |
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235 | (1) |
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235 | (2) |
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Chapter Notes and Further Reading |
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237 | (8) |
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238 | (3) |
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241 | (4) |
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Numerical Solutions and Conditioning of Lyapunov and Sylvester Equations |
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245 | (60) |
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245 | (2) |
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The Existence and Uniqueness of Solutions |
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247 | (2) |
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The Sylvester Equation: XA + BX = C |
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247 | (1) |
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The Lyapunov Equation: XA + ATX = C |
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248 | (1) |
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The Discrete Lyapunov Equation: ATX A -- X = C |
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248 | (1) |
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Perturbation Analysis and the Condition Numbers |
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249 | (13) |
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Perturbation Analysis for the Sylvester Equation |
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249 | (2) |
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The Condition Number of the Sylvester Equation |
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251 | (1) |
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Perturbation Analysis for the Lyapunov Equation |
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252 | (1) |
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The Condition Number of the Lyapunov Equation |
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253 | (1) |
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Sensitivity of the Stable Lyapunov Equation |
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253 | (4) |
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Sensitivity of the Discrete Lyapunov Equation |
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257 | (1) |
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Sensitivity of the Stable Discrete Lyapunov Equation |
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257 | (1) |
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Determining Ill-Conditioning from the Eigenvalues |
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258 | (2) |
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A Condition Number Estimator for the Sylvester Equation: ATX -- XB = C |
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260 | (2) |
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Analytical Methods for the Lyapunov Equations: Explicit Expressions for Solutions |
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262 | (1) |
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Numerical Methods for the Lyapunov and Sylvester Equations |
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263 | (21) |
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Numerical Instability of Diagonalization, Jordan Canonical Form, and Companion Form Techniques |
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264 | (1) |
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The Schur Method for the Lyapunov Equation: XA + ATX = C |
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265 | (4) |
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The Hessenberg-Schur Method for the Sylvester Equation |
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269 | (5) |
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The Schur Method for the Discrete Lyapunov Equation |
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274 | (2) |
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Residual and Backward Error in the Schur and Hessenberg--Schur Algorithms |
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276 | (2) |
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A Hessenberg Method for the Sylvester Equation: AX + XB = C |
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278 | (5) |
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The Hessenberg-Schur Method for the Discrete Sylvester Equation |
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283 | (1) |
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Direct Computations of the Cholesky Factors of Symmetric Positive Definite Solutions of Lyapunov Equations |
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284 | (9) |
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Computing the Cholesky Factor of the Positive Definite Solution of the Lyapunov Equation |
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284 | (5) |
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Computing the Cholesky Factor of the Positive Definite Solution of the Discrete Lyapunov Equation |
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289 | (4) |
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Comparisions of Different Methods and Conclusions |
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293 | (1) |
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293 | (3) |
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Matlab Control System Toolbox |
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293 | (1) |
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293 | (1) |
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294 | (1) |
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294 | (1) |
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295 | (1) |
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295 | (1) |
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296 | (1) |
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Chapter Notes and Further Reading |
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297 | (8) |
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298 | (3) |
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301 | (4) |
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PART III CONTROL SYSTEMS DESIGN |
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305 | (342) |
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Realization and Subspace Identification |
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307 | (36) |
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307 | (1) |
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State-Space Realizations of a Transfer Function |
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308 | (6) |
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Controllable and Observable Realizations |
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309 | (1) |
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310 | (4) |
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Computing Minimal Realizations from Markov Parameters |
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314 | (10) |
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Some Basic Properties of the Hankel Matrix of Markov Parameters |
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315 | (1) |
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An SVD Method for Minimal Realization |
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316 | (3) |
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A Modified SVD Method for Minimal Realization |
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319 | (5) |
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Subspace Identification Algorithms |
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324 | (10) |
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A Subspace Deterministic Model Identification Algorithm |
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324 | (5) |
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A Stochastic Subspace Model Identification Algorithm |
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329 | (3) |
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Continuous-Time System Identification |
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332 | (1) |
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Frequency-Domain Identification |
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332 | (2) |
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334 | (1) |
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Matlab Control System Toolbox |
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334 | (1) |
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334 | (1) |
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334 | (1) |
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335 | (1) |
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335 | (1) |
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335 | (2) |
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Chapter Notes and Further Reading |
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337 | (6) |
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337 | (3) |
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340 | (3) |
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Feedback Stabilization, Eigenvalue Assignment, and Optimal Control |
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343 | (62) |
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343 | (2) |
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State-Feedback Stabilization |
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345 | (8) |
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Stabilizability and Controllability |
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346 | (2) |
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Stabilization via Lyapunov Equations |
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348 | (5) |
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353 | (1) |
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Eigenvalue and Eigenstructure Assignment Problems |
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354 | (9) |
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Eigenvalue Assignment by State Feedback |
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358 | (3) |
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Eigenvalue Assignment by Output Feedback |
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361 | (1) |
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Eigenstructure Assignment |
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361 | (2) |
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The Quadratic Optimization Problems |
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363 | (10) |
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The Continuous-Time Linear Quadratic Regulator (LQR) Problem |
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364 | (8) |
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The Discrete-Time Linear Quadratic Regulator Problem |
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372 | (1) |
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373 | (13) |
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375 | (6) |
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H∞-Control Problem: A State-Feedback Case |
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381 | (2) |
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The H∞-Control Problem: Output Feedback Case |
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383 | (3) |
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The Complex Stability Radius and Riccati Equation |
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386 | (5) |
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391 | (2) |
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Matlab Control System Toolbox |
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391 | (1) |
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391 | (1) |
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392 | (1) |
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392 | (1) |
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392 | (1) |
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393 | (4) |
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Chapter Notes and Further Reading |
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397 | (8) |
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398 | (3) |
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401 | (4) |
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Numerical Methods and Conditioning of the Eigenvalue Assignment Problems |
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405 | (64) |
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405 | (2) |
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Numerical Methods for the Single-input Eigenvalue Assignment Problem |
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407 | (14) |
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A Recursive Algorithm for the Single-Input Problem |
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410 | (4) |
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An Error Analysis of the Recursive Single-Input Method |
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414 | (2) |
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The QR and RQ Implementations of Algorithm 11.2.1 |
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416 | (4) |
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Explicit and Implicit RQ Algorithms |
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420 | (1) |
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Numerical Methods for the Multi-input Eigenvalue Assignment Problem |
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421 | (18) |
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A Recursive Multi-Input Eigenvalue Assignment Algorithm |
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422 | (3) |
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The Explicit QR Algorithm for the Multi-Input EVA Problem |
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425 | (4) |
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The Schur Method for the Multi-Input Eigenvalue Assignment Problem |
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429 | (7) |
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Partial Eigenvalue Assignment Problem |
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436 | (3) |
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Conditioning of the Feedback Problem |
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439 | (4) |
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439 | (1) |
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440 | (1) |
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Absolute and Relative Condition Numbers |
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441 | (2) |
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Conditioning of the Closed-loop Eigenvalues |
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443 | (2) |
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Robust Eigenvalue Assignment |
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445 | (7) |
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445 | (1) |
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Statement and Existence of Solution of the Robust EigenValue Assignment Problem |
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446 | (1) |
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A Solution Technique for the Robust Eigenvalue Assignment Problem |
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447 | (5) |
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Comparison of Efficiency and Stability: the Single-input EVA Problem |
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452 | (1) |
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Comparison of Efficiency and Stability: the Multi-input EVA Problem |
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453 | (1) |
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Comparative Discussion of Various Methods and Recommendation |
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453 | (2) |
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455 | (1) |
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Matlab Control System Toolbox |
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455 | (1) |
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455 | (1) |
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455 | (1) |
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456 | (1) |
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456 | (1) |
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456 | (1) |
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456 | (3) |
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Chapter Notes and Further Reading |
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459 | (10) |
|
|
|
460 | (4) |
|
|
|
464 | (5) |
|
State Estimation: Observer and the Kalman Filter |
|
|
469 | (50) |
|
|
|
469 | (1) |
|
State Estimation via Eigenvalue Assignment |
|
|
470 | (1) |
|
State Estimation via Sylvester Equation |
|
|
471 | (3) |
|
Reduced-order State Estimation |
|
|
474 | (8) |
|
Reduced-Order State Estimation via Eigenvalue Assignment |
|
|
474 | (5) |
|
Reduced-Order State Estimation via Sylvester-Observer Equation |
|
|
479 | (3) |
|
Combined State Feedback and Observer Design |
|
|
482 | (1) |
|
Characterization of Nonsingular Solutions of the Sylvester Equation |
|
|
483 | (2) |
|
Numerical Solutions of the Sylvester-Observer Equation |
|
|
485 | (11) |
|
A Recursive Method for the Hessenberg Sylvester-Observer Equation |
|
|
486 | (4) |
|
A Recursive Block-Triangular Algorithm for the Hessenberg Sylvester-Observer Equation |
|
|
490 | (6) |
|
Numerical Solutions of a Constrained Sylvester-observer Equation |
|
|
496 | (3) |
|
Optimal State Estimation: The Kalman Filter |
|
|
499 | (6) |
|
The Linear Quadratic Gaussian Problem |
|
|
505 | (4) |
|
|
|
509 | (1) |
|
Matlab Control System Toolbox |
|
|
509 | (1) |
|
|
|
509 | (1) |
|
|
|
509 | (1) |
|
|
|
509 | (1) |
|
|
|
510 | (1) |
|
|
|
510 | (3) |
|
Chapter Notes and Further Reading |
|
|
513 | (6) |
|
|
|
514 | (2) |
|
|
|
516 | (3) |
|
Numerical Solutions and Conditioning of Algebraic Riccati Equations |
|
|
519 | (82) |
|
|
|
519 | (2) |
|
The Existence and Uniqueness of the Stabilizing Solution of the Care |
|
|
521 | (8) |
|
The Existence and Uniqueness of the Stabilizing Solution of the Dare |
|
|
529 | (1) |
|
Conditioning of the Riccati Equations |
|
|
530 | (9) |
|
|
|
531 | (6) |
|
|
|
537 | (2) |
|
Computational Methods for Riccati Equations |
|
|
539 | (40) |
|
The Eigenvector and Schur Vector Methods |
|
|
540 | (10) |
|
The Generalized Eigenvector and Schur Vector Methods |
|
|
550 | (10) |
|
The Matrix Sign Function Methods |
|
|
560 | (6) |
|
|
|
566 | (13) |
|
The Schur and Inverse-Free Generalized Schur Methods for the Descriptor Riccati Equations |
|
|
579 | (2) |
|
The Generalized Schur Method for the DCARE |
|
|
580 | (1) |
|
The Inverse-Free Generalized Schur Method for the DCARE |
|
|
581 | (1) |
|
The Inverse-Free Generalized Schur Method for the DDARE |
|
|
581 | (1) |
|
Conclusions and Table of Comparisons |
|
|
581 | (2) |
|
|
|
583 | (2) |
|
Matlab Control System Toolbox |
|
|
583 | (1) |
|
|
|
583 | (1) |
|
|
|
584 | (1) |
|
|
|
584 | (1) |
|
|
|
585 | (1) |
|
|
|
585 | (3) |
|
Chapter Notes and Further Reading |
|
|
588 | (13) |
|
|
|
591 | (2) |
|
|
|
593 | (8) |
|
Internal Balancing and Model Reduction |
|
|
601 | (46) |
|
|
|
601 | (1) |
|
Internal Balancing for Continuous-time Systems |
|
|
602 | (7) |
|
Internal Balancing of a Minimal Realization (MR) |
|
|
603 | (3) |
|
Internal Balancing of a Nonminimal Realization |
|
|
606 | (3) |
|
Internal Balancing for Discrete-time Systems |
|
|
609 | (2) |
|
|
|
611 | (12) |
|
Model Reduction via Balanced Truncation |
|
|
611 | (4) |
|
The Schur Method for Model Reduction |
|
|
615 | (6) |
|
A Balancing-Free Square-Root Method for Model Reduction |
|
|
621 | (2) |
|
Hankel-Norm Approximations |
|
|
623 | (10) |
|
A Characterization of All Solutions to the optional Hankel-Norm Approximation |
|
|
624 | (9) |
|
Model Reduction of an Unstable System |
|
|
633 | (1) |
|
Frequency-Weighted Model Reduction |
|
|
633 | (2) |
|
Summary and Comparisons of Model Reduction Procedures |
|
|
635 | (1) |
|
|
|
636 | (2) |
|
Matlab Control System Toolbox |
|
|
636 | (1) |
|
|
|
637 | (1) |
|
|
|
637 | (1) |
|
|
|
637 | (1) |
|
|
|
637 | (1) |
|
|
|
638 | (2) |
|
Chapter Notes and Further Reading |
|
|
640 | (7) |
|
|
|
641 | (4) |
|
|
|
645 | (2) |
|
|
|
647 | (22) |
|
Large-Scale Matrix Computations in Control: Krylov Subspace Methods |
|
|
649 | (20) |
|
|
|
649 | (1) |
|
The Arnoldi and Block Arnoldi Methods |
|
|
650 | (3) |
|
The Scalar Arnoldi Method |
|
|
650 | (1) |
|
|
|
650 | (1) |
|
The Lanczos and Block Lanczos Methods |
|
|
651 | (2) |
|
Scopes of using the Krylov Subspace Methods in Control |
|
|
653 | (1) |
|
Arnoldi Methods for Lyapunov, Sylvester, and Algebraic Riccati Equations |
|
|
653 | (6) |
|
Arnoldi Method for Partial Eigenvalue Assignment |
|
|
659 | (1) |
|
Lanczos and Arnoldi Methods for Model Reduction |
|
|
659 | (3) |
|
Lanczos Methods for Model Reduction |
|
|
660 | (1) |
|
Block Lanczos and Band Lanczos Methods for MIMO Model Reduction |
|
|
661 | (1) |
|
An Arnoldi Method for SISO Model Reduction |
|
|
661 | (1) |
|
Chapter Notes and Further Reading |
|
|
662 | (7) |
|
|
|
663 | (1) |
|
|
|
663 | (6) |
|
APPENDIX A SOME EXISTING SOFTWARE FOR CONTROL SYSTEMS DESIGN AND ANALYSIS |
|
|
669 | (4) |
|
A.1 Matlab Control System Toolbox |
|
|
669 | (1) |
|
|
|
669 | (1) |
|
A.3 Control System Professional---Advanced Numerical Methods (CSP-ANM) |
|
|
670 | (1) |
|
|
|
670 | (1) |
|
|
|
671 | (1) |
|
A.6 System Identification Software |
|
|
671 | (2) |
|
A.6.1 MATLAB System Identification Toolbox |
|
|
671 | (1) |
|
A.6.2 Xmath Interactive System Identification Module, Part-2 |
|
|
671 | (1) |
|
|
|
671 | (1) |
|
|
|
672 | (1) |
|
APPENDIX B MATCONTROL AND LISTING OF MATCONTROL FILES |
|
|
673 | (6) |
|
|
|
673 | (1) |
|
B.2 Chapterwise Listing of Matcontrol Files |
|
|
674 | (5) |
|
APPENDIX C CASE STUDY: CONTROL OF A 9-STATE AMMONIA REACTOR |
|
|
679 | (10) |
|
|
|
679 | (1) |
|
C.2 Testing the controllability |
|
|
680 | (1) |
|
C.3 Testing the Observability |
|
|
680 | (1) |
|
C.4 Testing the Stability |
|
|
681 | (1) |
|
C.5 Lyapunov Stabilization |
|
|
681 | (1) |
|
C.6 Pole-Placement Design |
|
|
682 | (1) |
|
C.7 The LQR and LQG Designs |
|
|
682 | (3) |
|
C.8 State-Estimation(observer): Kalman estimator versus Sylvester Estimator |
|
|
685 | (1) |
|
C.9 System Identification and Model Reduction |
|
|
686 | (3) |
|
|
|
688 | (1) |
| Index |
|
689 | |
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