Stability and Stabilization

An Introduction

William J. Terrell

• Publisher: Princeton University Press
• Year: 2009
• Print ISBN: 9780691134444
• eBook ISBN: 9781400833351
• Topic: Mathematics
• Subtopic: Linear Algebra
• Index: Mathematics

Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations. Designed for advanced undergraduates and beginning graduate students in the sciences, engineering, and mathematics, the book takes a unique modern approach that bridges the gap between linear and nonlinear systems.


Presenting stability and stabilization of equilibria as a core problem of mathematical control theory, the book emphasizes the subject's mathematical coherence and unity, and it introduces and develops many of the core concepts of systems and control theory. There are five chapters on linear systems and nine chapters on nonlinear systems; an introductory chapter; a mathematical background chapter; a short final chapter on further reading; and appendixes on basic analysis, ordinary differential equations, manifolds and the Frobenius theorem, and comparison functions and their use in differential equations. The introduction to linear system theory presents the full framework of basic state-space theory, providing just enough detail to prepare students for the material on nonlinear systems.

• Focuses on stability and feedback stabilization


• Bridges the gap between linear and nonlinear systems for advanced undergraduates and beginning graduate students


• Balances coverage of linear and nonlinear systems


• Covers cascade systems


• Includes many examples and exercises

Table of contents

• Cover
• Title
• Copyright
• Contents
• List of Figures
• Preface
• 1 Introduction
• 2 Mathematical Background
• 3 Linear Systems and Stability
• 4 Controllability of Linear Time Invariant Systems
• 5 Observability and Duality
• 6 Stabilizability of LTI Systems
• 7 Detectability and Duality
• 8 Stability Theory
• 9 Cascade Systems
• 10 Center Manifold Theory
• 11 Zero Dynamics
• 12 Feedback Linearization of Single-Input Nonlinear Systems
• 13 An Introduction to Damping Control
• 14 Passivity
• 15 Partially Linear Cascade Systems
• 16 Input-to-State Stability
• 17 Some Further Reading
• Appendix A Notation: A Brief Key
• Appendix B Analysis in R and R^n
• Appendix C Ordinary Differential Equations
• Appendix D Manifolds and the Preimage Theorem; Distributions and the Frobenius Theorem
• Appendix E Comparison Functions and a Comparison Lemma
• Appendix F Hints and Solutions for Selected Exercises
• Bibliography
• Index