Linear Systems Theory

by Chen, Ben M.; Lin, Zongli; SHAMASH, YACOV

• ISBN13: 9780817637798
• ISBN10: 0817637796
• Format: Hardcover
• Copyright: 2004-10-30
• Publisher: Birkhauser

Summary

This text is the first comprehensive treatment of structural decompositions of various types of linear systems, including autonomous, unforced or unsensed, strictly proper, non-strictly proper, and descriptor or singular systems. Structural properties play an important role in the understanding of linear systems and also provide insight to facilitate the solution of control problems related to stabilization, disturbance decoupling, robust and optimal control. Applications can be extended to industrial process control, aircraft and ship control, process automation control, and many other types of engineering systems.The authors employ a unique structural decomposition approach to break down an overall system into various subsystems, each with distinct features. The simplicity of these subsystems and their interconnections lead to deep insight about the design of feedback control systems for desired closed-loop performance, stability, and robustness. All results and case studies are presented in both continuous- and discrete-time settings. Exercises, as well as MATLAB-based computational and design algorithms utilizing the Linear Systems Toolkit, are included to reinforce and demonstrate the concepts treated throughout the book.Topics covered include:* Basic Concepts of Linear Systems Theory* Decomposition of Unforced and/or Unsensed Systems, Proper Systems and their Properties* Decomposition of Descriptor Systems and their Properties* Cascade and Inner-Outer Factorizations* Structural Assignment through Sensor/Actuator Selections* State Feedback Control with Time-Scale and Eigenstructure Assignment* Disturbance Decoupling with Static Output FeedbackLinear Systems Theory may be used as a textbook for advanced undergraduate and graduate students in aeronautics and astronautics, applied mathematics, chemical, electrical and mechanical engineering. It may also serve as a valuable self-study reference for researchers and engineering practitioners in areas related to systems and control theory.

Table of Contents

Preface	xi
Introduction and Preview	1	(8)
Motivation	1	(2)
Preview of Each Chapter	3	(3)
Notation	6	(3)
Mathematical Background	9	(22)
Introduction	9	(1)
Vector Spaces and Subspaces	9	(3)
Matrix Algebra and Properties	12	(14)
Determinant, Inverse and Differentiation	13	(2)
Rank, Eigenvalues and Jordan Form	15	(3)
Special Matrices	18	(4)
Singular Value Decomposition	22	(4)
Norms	26	(5)
Norms of Vectors	26	(1)
Norms of Matrices	26	(1)
Norms of Continuous-time Signals	27	(1)
Norms of Discrete-time Signals	28	(1)
Norms of Continuous-time Systems	28	(1)
Norms of Discrete-time Systems	29	(2)
Review of Linear Systems Theory	31	(38)
Introduction	31	(2)
Dynamical Responses	33	(2)
System Stability	35	(5)
Controllability and Observability	40	(7)
System Invertibilities	47	(2)
Normal Rank, Finite Zeros and Infinite Zeros	49	(6)
Geometric Subspaces	55	(6)
Properties of State Feedback and Output Injection	61	(3)
Exercises	64	(5)
Decompositions of Unforced and/or Unsensed Systems	69	(38)
Introduction	69	(1)
Autonomous Systems	70	(9)
Unforced Systems	79	(16)
Unsensed Systems	95	(8)
Exercises	103	(4)
Decompositions of Proper Systems	107	(82)
Introduction	107	(1)
SISO Systems	108	(9)
Strictly Proper Systems	117	(36)
Nonstrictly Proper Systems	153	(10)
Proofs of Properties of Structural Decomposition	163	(11)
Kronecker and Smith Forms of the System Matrix	174	(7)
Discrete-time Systems	181	(2)
Exercises	183	(6)
Decompositions of Descriptor Systems	189	(38)
Introduction	189	(4)
SISO Descriptor Systems	193	(8)
MIMO Descriptor Systems	201	(7)
Proofs of Theorem 6.3.1 and Its Properties	208	(13)
Discrete-time Descriptor Systems	221	(2)
Exercises	223	(4)
Structural Mappings of Bilinear Transformations	227	(30)
Introduction	227	(1)
Mapping of Continuous- to Discrete-time Systems	228	(7)
Mapping of Discrete- to Continuous-time Systems	235	(5)
Proof of Theorem 7.2.1	240	(15)
Exercises	255	(2)
System Factorizations	257	(30)
Introduction	257	(2)
Strictly Proper Systems	259	(10)
Nonstrictly Proper Systems	269	(9)
Discrete-time Systems	278	(6)
Exercises	284	(3)
Structural Assignment via Sensor/Actuator Selection	287	(26)
Introduction	287	(2)
Simultaneous Finite and Infinite Zero Placement	289	(8)
SISO Systems	289	(4)
MIMO Systems	293	(4)
Complete Structural Assignment	297	(12)
Exercises	309	(4)
Time-Scale and Eigenstructure Assignment via State Feedback	313	(28)
Introduction	313	(1)
Continuous-time Systems	314	(18)
Design Procedures and Fundamental Properties	314	(11)
H2 Control, H∞ Control and Disturbance Decoupling	325	(7)
Discrete-time Systems	332	(5)
Design Procedures and Fundamental Properties	332	(2)
H2 Control, H∞ Control and Disturbance Decoupling	334	(3)
Exercises	337	(4)
Disturbance Decoupling with Static Output Feedback	341	(26)
Introduction	341	(2)
Left Invertible Systems	343	(6)
General Multivariable Systems	349	(17)
Exercises	366	(1)
A Software Toolkit	367	(28)
Introduction	367	(2)
Descriptions of m-Functions	369	(26)
Decompositions of Autonomous Systems	370	(1)
Decompositions of Unforced and Unsensed Systems	371	(3)
Decompositions and Properties of Proper Systems	374	(6)
Operations of Vector Subspaces	380	(1)
Decompositions and Properties of Descriptor Systems	381	(2)
System Factorizations	383	(2)
Structural Assignment via Sensor/Actuator Selection	385	(1)
State Feedback Control with Eigenstructure Assignment	386	(7)
Disturbance Decoupling with Static Output Feedback	393	(2)
Bibliography	395	(14)
Index	409