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Stability and Stabilization of Nonlinear Systems

Benefits

  • Provides readers with a general framework for the previously disparate mathematical methods associated with a vital aspect of control theory

  • Gives concrete examples of stability theory for real nonlinear systems including biological and economic systems

  • Written by experts

Book

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 1-54
  3. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 55-122
  4. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 123-142
  5. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 143-202
  6. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 203-260
  7. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 261-353
  8. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 355-379
  9. Iasson Karafyllis, Zhong-Ping Jiang
    Pages 381-384
  10. Back Matter
    Pages 385-386

About this book

Introduction

Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of stability and feedback stabilization methods, which enables the reader to learn and understand major techniques used in mathematical control theory.

In particular:

• the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization;

• a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems;

• approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and

• new tools for stability analysis and control design of a wide class of nonlinear systems are introduced.

The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples.

Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.

Keywords

Control Engineering Control Theory Feedback Stabilization Input-to-state Stability Lyapunov Functions Small-gain Analysis

Authors and affiliations

  1. 1.Department of Environmental EngineeringTechnical University of CreteChaniaGreece
  2. 2.Polytechnic Inst., Dept. Electrical & Computer EngineeringNew York UniversityBrooklynUSA

Bibliographic information

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Reviews

From the reviews:

“The book is presented in a logical order and is self-contained. … Each chapter contains a section with bibliographical and historical notes … and each closes with a comprehensive list of references … . Overall, for a graduate student of systems and control this book will provide an in-depth course on a general theory of nonlinear control systems with many references to further literature and an indication of open research problems. As a reference text, this book will certainly also be useful to control researchers.” (Björn S. Rüffer, Mathematical Reviews, Issue 2012 d)

“In this research monograph, the authors give an account of the results on stability and stabilizability which have been obtained over the last years. They do this for a large class of systems. Their class of systems include nonlinear ordinary differential equations, but also nonlinear difference equations, and nonlinear delay differential equations. … The book gives a clear account of the theory up to today.” (Hans Zwart, Zentralblatt MATH, Vol. 1243, 2012)