Linear Systems Theory

A Structural Decomposition Approach

Ben M. Chen, National University of Singapore
Zongli Lin, University of Virginia
Yacov Shamash, State University of New York at Stony Brook

Birkhauser, Boston, 2004 (¥ click on this link to order ¥)

Control Engineering Series, xiii/415 pages / ISBN 0-81763-779-6    ... Errata List ...

From the Back Cover:

This text is the first comprehensive treatment of structural decompositions of various types of linear systems, including autonomous, unforced or unsensed, strictly proper, nonstrictly 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:

Linear 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} 
 
   1 Introduction and Preview  {1} 
     1.1 Motivation
     1.2 Preview of Each Chapter
     1.3 Notation
 
   2 Mathematical Background  {9} 
     2.1 Introduction
     2.2 Vector Spaces and Subspaces 
     2.3 Matrix Algebra and Properties 
         2.3.1 Determinant, Inverse and Differentiation 
         2.3.2 Rank, Eigenvalues and Jordan Form 
         2.3.3 Special Matrices 
         2.3.4 Singular Value Decomposition 
     2.4 Norms 
         2.4.1 Norms of Vectors 
         2.4.2 Norms of Matrices 
         2.4.3 Norms of Continuous-time Signals 
         2.4.4 Norms of Discrete-time Signals 
         2.4.5 Norms of Continuous-time Systems 
         2.4.6 Norms of Discrete-time Systems 
 
   3 Review of Linear Systems Theory  {31} 
     3.1 Introduction 
     3.2 Dynamical Responses
     3.3 System Stability 
     3.4 Controllability and Observability 
     3.5 System Invertibilities 
     3.6 Normal Rank, Finite Zeros and Infinite Zeros 
     3.7 Geometric Subspaces 
     3.8 Properties of State Feedback and Output Injection 
     3.9 Exercises 
 
   4 Decompositions of Unforced and/or Unsensed Systems  {69}  
     4.1 Introduction 
     4.2 Autonomous Systems 
     4.3 Unforced Systems 
     4.4 Unsensed Systems 
     4.5 Exercises 
 
   5 Decompositions of Proper Systems  {107} 
     5.1 Introduction 
     5.2 SISO Systems 
     5.3 Strictly Proper Systems 
     5.4 Non-Strictly Proper Systems 
     5.5 Proofs of Properties of Structural Decomposition 
     5.6 Kronecker and Smith Forms of the System Matrix 
     5.7 Discrete-time Systems
     5.8 Exercises 
 
   6 Decompositions of Descriptor Systems  {189} 
     6.1 Introduction 
     6.2 SISO Descriptor Systems 
     6.3 MIMO Descriptor Systems 
     6.4 Proofs of Theorem 6.3.1 and Its Properties 
     6.5 Discrete-time Descriptor Systems
     6.6 Exercises 
 
   7 Structural Mappings of Bilinear Transformations  {227} 
     7.1 Introduction 
     7.2 Mapping of Continuous- to Discrete-time Systems 
     7.3 Mapping of Discrete- to Continuous-time Systems 
     7.4 Proof of Theorem 7.2.1 
     7.5 Exercises 
 
   8 System Factorizations  {257} 
     8.1 Introduction 
     8.2 Strictly Proper Systems 
     8.3 Non-Strictly Proper Systems 
     8.4 Discrete-time Systems 
     8.5 Exercises 
 
   9 Structural Assignment via Sensor/Actuator Selection  {287} 
     9.1 Introduction 
     9.2 Simultaneous Finite and Infinite Zero Placement
         9.2.1 SISO Systems 
         9.2.2 MIMO Systems 
     9.3 Complete Structural Assignment
     9.4 Exercises
 
  10 Time-Scale and Eigenstructure Assignment via State Feedback  {313} 
     10.1 Introduction 
     10.2 Continuous-time Systems 
          10.2.1 Design Procedures and Fundamental Properties 
          10.2.2 H2, H∞ Control and Disturbance Decoupling
     10.3 Discrete-time Systems 
          10.3.1 Design Procedures and Fundamental Properties 
          10.3.2 H2, H∞ Control and Disturbance Decoupling
     10.4 Exercises 
 
  11 Disturbance Decoupling with Static Output Feedback  {341} 
     11.1 Introduction 
     11.2 Left Invertible Systems 
     11.3 General Multivariable Systems 
     11.4 Exercises
 
  12 A Software Toolkit  {367}
     12.1 Introduction 
     12.2 Descriptions of m-Functions 
          12.2.1 Decompositions of Autonomous Systems 
          12.2.2 Decompositions of Unforced and Unsensed Systems
          12.2.3 Decompositions and Properties of Proper Systems
          12.2.4 Operations of Vector Subspaces
          12.2.5 Decompositions and Properties of Descriptor Systems
          12.2.6 System Factorizations
          12.2.7 Structural Assignment via Sensor/Actuator Selection
          12.2.8 State Feedback Control with Eigenstructure Assignment
          12.2.9 Disturbance Decoupling with Static Output Feedback
 
     Bibliography  {395} 
 
     Index  {409} 
 

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