Lyapunov Matrix Equation in System Stability and Control

Zoran Gajić and Muhammad Tahir Javed Qureshi (Eds.)0122733703, 9780122733703, 9780080535678

The Lyapunov and Riccati equations are two of the fundamental equations of control and system theory, having special relevance for system identification, optimization, boundary value problems, power systems, signal processing, and communications. The Lyapunov Matrix Equation in System Stability and Control covers mathematical developments and applications while providing quick and easy references for solutions to engineering and mathematical problems. Examples of real-world systems are given throughout the text in order to demonstrate the effectiveness of the presented methods and algorithms. The book will appeal to practicing engineers, theoreticians, applied mathematicians, and graduate students who seek a comprehensive view of the main results of the Lyapunov matrix equation. Presents techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems Offers summaries and references at the end of each chapter Contains examples of the use of the equation to solve real-world problems Provides quick and easy references for the solutions to engineering and mathematical problems using the Lyapunov equation

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Table of contents :
Content:
Preface
Pages xi-xii
Z. Gajić, M. Qureshi

Chapter One Introduction
Pages 1-20

Chapter Two Continuous algebraic Lyapunov equation Original Research Article
Pages 21-77

Chapter Three Discrete algebraic Lyapunov equation Original Research Article
Pages 79-106

Chapter Four Differential and difference Lyapunov equations Original Research Article
Pages 107-132

Chapter Five Algebraic Lyapunov equations with small parameters Original Research Article
Pages 133-153

Chapter Six Stability robustness and sensitivity of Lyapunov equation Original Research Article
Pages 155-167

Chapter Seven Iterative methods and parallel algorithms Original Research Article
Pages 169-188

Chapter Eight Lyapunov iterations Original Research Article
Pages 189-222

Chapter Nine Concluding remarks Original Research Article
Pages 223-241

Appendix Matrix inequalities
Pages 243-249

Index
Pages 251-255