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9780195117776

Linear System Theory and Design

by
  • ISBN13:

    9780195117776

  • ISBN10:

    0195117778

  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 1998-09-10
  • Publisher: Oxford University Press
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List Price: $163.14

Summary

An extensive revision of the author's highly successful text, this third edition of Linear System Theory and Design has been made more accessible to students from all related backgrounds. After introducing the fundamental properties of linear systems, the text discusses design using stateequations and transfer functions. In state-space design, Lyapunov equations are used extensively to design state feedback and state estimators. In the discussion of transfer-function design, pole placement, model matching, and their applications in tracking and disturbance rejection are covered.Both one-and two-degree-of-freedom configurations are used. All designs can be accomplished by solving sets of linear algebraic equations. The two main objectives of the text are to: DT use simple and efficient methods to develop results and design procedures DT enable students to employ the results to carry out design All results in this new edition are developed for numerical computation and illustrated using MATLAB, with an emphasis on the ideas behind the computation and interpretation of results. This book develops all theorems and results in a logical way so that readers can gain an intuitive understandingof the theorems. This revised edition begins with the time-invariant case and extends through the time-varying case. It also starts with single-input single-output design and extends to multi-input multi-output design. Striking a balance between theory and applications, Linear System Theory andDesign, 3/e, is ideal for use in advanced undergraduate/first-year graduate courses in linear systems and multivariable system design in electrical, mechanical, chemical, and aeronautical engineering departments. It assumes a working knowledge of linear algebra and the Laplace transform and anelementary knowledge of differential equations.

Table of Contents

Preface xi
Chapter 1: Introduction
1(4)
1.1 Introduction
1(1)
1.2 Overview
2(3)
Chapter 2: Mathematical Descriptions of Systems
5(39)
2.1 Introduction
5(2)
2.1.1 Causaliity and Lumpedness
6(1)
2.2 Linear Systems
7(4)
2.3 Linear Time-Invariant (LTI) Systems
11(6)
2.3.1 Op-Amp Circuit Implementation
16(1)
2.4 Linearization
17(1)
2.5 Examples
18(13)
2.5.1 RLC Networks
26(5)
2.6 Discrete-Time Systems
31(6)
2.7 Concluding Remarks
37(1)
Problems
38(6)
Chapter 3: Linear Algebra
44(42)
3.1 Introduction
44(1)
3.2 Basis, Representation, and Orthonormalization
45(3)
3.3 Linear Algebraic Equations
48(5)
3.4 Similarity Transformation
53(2)
3.5 Diagonal Form and Jordan Form
55(6)
3.6 Functions of a Square Matrix
61(9)
3.7 Lyapunov Equation
70(1)
3.8 Some Useful Formulas
71(2)
3.9 Quadratic Form and Positive Definiteness
73(3)
3.10 Singular-Value Decomposition
76(2)
3.11 Norms of Matrices
78(1)
Problems
78(8)
Chapter 4: State-Space Solutions and Realizations
86(35)
4.1 Introduction
86(1)
4.2 Solution of LTI State Equations
87(6)
4.2.1 Discretization
90(2)
4.2.2 Solution of Discrete-Time Equations
92(1)
4.3 Equivalent State Equations
93(7)
4.3.1 Canonical Forms
97(1)
4.3.2 Magnitude Scaling in Op-Amp Circuits
98(2)
4.4 Realizations
100(6)
4.5 Solution of Linear Time-Varying (LTV) Equations
106(5)
4.5.1 Discrete-Time Case
110(1)
4.6 Equivalent Time-Varying Equations
111(4)
4.7 Time-Varying Realizations
115(2)
Problems
117(4)
Chapter 5: Stability
121(22)
5.1 Introduction
121(1)
5.2 Input-Output Stability of LTI Systems
121(8)
5.2.1 Discrete-Time Case
126(3)
5.3 Internal Stability
129(3)
5.3.1 Discrete-Time Case
131(1)
5.4 Lyapunov Theorem
132(5)
5.4.1 Discrete-Time Case
135(2)
5.5 Stability of LTV Systems
137(3)
Problems
140(3)
Chapter 6: Controllability and Observability
143(41)
6.1 Introduction
143(1)
6.2 Controllability
144(9)
6.2.1 Controllablity Indices
150(3)
6.3 Observability
153(5)
6.3.1 Observability Indices
157(1)
6.4 Canonical Decomposition
158(6)
6.5 Conditions in Jordan-Form Equations
164(5)
6.6 Discrete-Time State Equations
169(3)
6.6.1 Controllability to the Origin and Reachability
171(1)
6.7 Controllability After Sampling
172(4)
6.8 LTV State Equations
176(4)
Problems
180(4)
Chapter 7: Minimal Realizations and Coprime Fractions
184(47)
7.1 Introduction
184(1)
7.2 Implications of Coprimeness
185(7)
7.2.1 Minimal Realizations
189(3)
7.3 Computing Coprime Fractions
192(5)
7.3.1 QR Decomposition
195(2)
7.4 Balanced Realization
197(3)
7.5 Realizations from Markov Parameters
200(5)
7.6 Degree of Transfer Matrices
205(2)
7.7 Minimal Realizations--Matrix Case
207(2)
7.8 Matrix Polynomial Fractions
209(11)
7.8.1 Column and Row Reducedness
212(2)
7.8.2 Computing Matrix Coprime Fractions
214(6)
7.9 Realizations from Matrix Coprime Fractions
220(5)
7.10 Realizations from Matrix Markov Parameters
225(2)
7.11 Concluding Remarks
227(1)
Problems
228(3)
Chapter 8: State Feedback and State Estimators
231(38)
8.1 Introduction
231(1)
8.2 State Feedback
232(10)
8.2.1 Solving the Lyapunov Equation
239(3)
8.3 Regulation and Tracking
242(5)
8.3.1 Robust Tracking and Disturbance Rejection
243(4)
8.3.2 Stabilization
247(1)
8.4 State Estimator
247(6)
8.4.1 Reduced-Dimensional State Estimator
251(2)
8.5 Feedback from Estimated States
253(2)
8.6 State Feedback--Multivariable Case
255(8)
8.6.1 Cyclic Design
256(3)
8.6.2 Lyapunov-Equation Method
259(1)
8.6.3 Canonical-Form Method
260(2)
8.6.4 Effect on Transfer Matrices
262(1)
8.7 State estimators--Multivariable Case
263(2)
8.8 Feedback from Estimated States--Multivariable Case
265(1)
Problems
266(3)
Chapter 9: Pole Placement and Model Matching
269(50)
9.1 Introduction
269(4)
9.1.1 Compensator Equations-Classical Method
271(2)
9.2 Unity-Feedback Configuration-Pole Placement
273(10)
9.2.1 Regulation and Tracking
275(2)
9.2.2 Robust Tracking and Disturbance Rejection
277(3)
9.2.3 Embedding Internal Models
280(3)
9.3 Implementable Transfer Functions
283(9)
9.3.1 Model Matching-Two-Parameter Configuration
286(5)
9.3.2 Implementation of Two-Parameter Compensators
291(1)
9.4 Multivariable Unity-Feedback Systems
292(14)
9.4.1 Regulation and Tracking
302(1)
9.4.2 Robust Tracking and Disturbance Rejection
303(3)
9.5 Multivariable Model Matching-Two-Parameter Configuration
306(8)
9.5.1 Decoupling
311(3)
9.6 Concluding Remarks
314(1)
Problems
315(4)
References 319(2)
Answers to Selected Problems 321(10)
Index 331

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