Stability and Stabilization : : An Introduction / / William J. Terrell.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Terrell, William J.,
• MitwirkendeR: Terrell, William J.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2009]; ©2009
• Year of Publication: 2009
• Language: English
• Physical Description: 1 online resource (480 p.) :; 14 line illus.

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

Frontmatter -- Contents -- List of Figures -- Preface -- Chapter One. Introduction -- Chapter Two. Mathematical Background -- Chapter Three. Linear Systems and Stability -- Chapter Four. Controllability of Linear Time Invariant Systems -- Chapter Five. Observability and Duality -- Chapter Six. Stabilizability of LTI Systems -- Chapter Seven. Detectability and Duality -- Chapter Eight. Stability Theory -- Chapter Nine. Cascade Systems -- Chapter Ten. Center Manifold Theory -- Chapter Eleven. Zero Dynamics -- Chapter Twelve. Feedback Linearization of Single-Input Nonlinear Systems -- Chapter Thirteen. An Introduction to Damping Control -- Chapter Fourteen. Passivity -- Chapter Fifteen. Partially Linear Cascade Systems -- Chapter Sixteen. Input-to-State Stability -- Chapter Seventeen. Some Further Reading -- Appendix A. Notation: A Brief Key -- Appendix B. Analysis in R and Rn -- 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