Stability and Stabilization of Nonlinear Systems

1. Front Matter

   Pages I-XIX

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2. Introduction to Control Systems

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 1-54

3. Internal Stability: Notions and Characterizations

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 55-122

4. Converse Lyapunov Results

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 123-142

5. External Stability: Notions and Characterizations

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 143-202

6. Advanced Stability Methods and Applications

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 203-260

7. Robust Output Feedback Stabilization

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 261-353

8. Applications

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 355-379

9. Open Problems

   • Iasson Karafyllis, Zhong-Ping Jiang

   Pages 381-384

10. Back Matter

    Pages 385-386

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Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization 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.

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

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)

• Department of Environmental Engineering, Technical University of Crete, Chania, Greece

  Iasson Karafyllis

• Polytechnic Inst., Dept. Electrical & Computer Engineering, New York University, Brooklyn, USA

  Zhong-Ping Jiang

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