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## Über dieses Buch

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.

## Inhaltsverzeichnis

### Chapter 1. Introduction to Control Systems

This introductory chapter begins with important classes of control systems that will be studied in greater details in subsequent chapters. Basic notions and preliminary results in mathematical system and control theories are presented. Practical examples arising from engineering, mathematical biology and economics are introduced and will be invoked in subsequent chapters.
Iasson Karafyllis, Zhong-Ping Jiang

### Chapter 2. Internal Stability: Notions and Characterizations

Chapter 2 is devoted to the analysis of internal (mainly global) stability notions used in mathematical control and systems theory. The stability notions presented are developed in the system-theoretic framework described in Chapter 1 so that one can obtain a wide perspective of the role of stability in various classes of deterministic systems possibly subject to exogenous disturbances.
Iasson Karafyllis, Zhong-Ping Jiang

### Chapter 3. Converse Lyapunov Results

Chapter 3 is devoted to answering the following question: do Lyapunov functionals always exist for a robustly globally asymptotically output stable system? The previous Chap. 2 showed that one of the most important ways of proving stability is the derivation of estimates which guarantee appropriate stability properties by means of Lyapunov functionals. The converse Lyapunov results obtained in this chapter show that such Lyapunov functionals always exist.
Iasson Karafyllis, Zhong-Ping Jiang

### Chapter 4. External Stability: Notions and Characterizations

Chapter 4 is devoted to the analysis of external global stability notions used in mathematical control and system theories. The presented stability notions are developed in the system-theoretic framework described in Chap. 1 so that one can obtain a wide perspective of the role of stability in various important classes of deterministic systems. The results in this chapter are of crucial importance from a practical point of view since almost all engineering and natural system are subject to external disturbance inputs, which may take differing forms as reference signals, actuator and sensor disturbances.
Iasson Karafyllis, Zhong-Ping Jiang

### Chapter 5. Advanced Stability Methods and Applications

Chapter 5 is devoted to the description of advanced analysis methods for checking the internal and external global stability properties introduced previously, for various important classes of nonlinear dynamic systems. A focus will be placed on small-gain techniques and vector Lyapunov functions.
Iasson Karafyllis, Zhong-Ping Jiang

### Chapter 6. Robust Output Feedback Stabilization

Chapter 6 is devoted to the study of the problem of robust output feedback stabilization for nonlinear systems. The emphasis is placed on nonlinear dynamical systems described by ODEs, by RFDEs and discrete-time systems and on disturbances and uncertainties taking the form of measurement noise, actuator noise and parameter variations. However, most of the presented results can be generalized to wider classes of uncertain control systems.
Iasson Karafyllis, Zhong-Ping Jiang

### Chapter 7. Applications

Chapter 7 aims to demonstrate the wide applicability of the analysis and synthesis tools presented in previous chapters. Three representative control problems are studied: (1) the stabilization of a delayed chemostat model; (2) the stabilization of numerical schemes for the numerical solution of systems described by ODEs; (3) the stabilization of the price of a commodity by manipulation of buffer stocks.
Iasson Karafyllis, Zhong-Ping Jiang

### Chapter 8. Open Problems

This chapter is devoted to the statement of some open problems in Mathematical Control Theory. It is the view of the authors that solving these open problems will require novel mathematical tools, and more importantly, contribute greatly to the further development of modern nonlinear control theory.
Iasson Karafyllis, Zhong-Ping Jiang

### Backmatter

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