- 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 Feedback

Zongli Lin, University of Virginia

Yacov Shamash, State University of New York at Stony Brook

Birkhauser, Boston, 2004 (click on this to order from the publisher)

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

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:

Preface {xi}1 Introduction and Preview {1}1.1 Motivation 1.2 Preview of Each Chapter 1.3 Notation2 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 Systems3 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 Exercises4 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 Exercises5 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 Exercises6 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 Exercises7 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 Exercises8 System Factorizations {257}8.1 Introduction 8.2 Strictly Proper Systems 8.3 Non-Strictly Proper Systems 8.4 Discrete-time Systems 8.5 Exercises9 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 Exercises10 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 Exercises11 Disturbance Decoupling with Static Output Feedback {341}11.1 Introduction 11.2 Left Invertible Systems 11.3 General Multivariable Systems 11.4 Exercises12 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 FeedbackBibliography {395}Index {409}