Stability of Dynamical Systems

Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of these major types of system models: finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. 

Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. 

The book covers the following four general topics:

* Representation and modeling of dynamical systems of the types described above
* Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces
* Specialization of this stability theory to finite-dimensional dynamical systems
* Specialization of this stability theory to infinite-dimensional dynamical systems

Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.

• Lagrange and
• actor
• continuous continuous-time systems
• continuous-time systems
• digital signal processing
• discontinuous continuous-time systems
• discrete-time systems
• dynamical systems
• finite-dimensional systems
• hybrid systems
• infinite-dimensional systems
• system
• ordinary differential equations
• partial differential equations

From the reviews:

"The book under review provides a single comprehensive source for the materials and results on stability analysis of all the dynamical systems … . contains numerous problems and suggestions for further study at the end of the main chapters. This book will be an excellent source of material for beginning graduate students studying the stability theory of dynamical systems and for self study by researchers and practitioners interested in systems theory of engineering, computer science, chemistry, life sciences and economics." (Olusola Akinyele, Mathematical Reviews, Issue 2008 i)

"The goal of this book is to provide a reference text for graduate students and researchers on stability theory for the class of systems encountered in modern applications. In this respect, the goal is indeed achieved since the book offers a self-contained presentation of stability theory.

…[In chapter 2] special care is taken to highlight the key concepts and ingredients, and an effort is made to consider all classes of systems that are relevant to applications. In addition, several important issues illustrating properties of solutions are highlighted by means of elementary, yet carefully selected, examples…The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems…[Chapters 6, 7, and 8] contain several nonstandard results and examples, thus making interesting reading even for experts.

…The use of this book as a reference text in stability theory is facilitated by an extensive index…In conclusion, Stability of Dynamical Systems: Continuous, Discontinuous, and Discrete Systems is a very interesting book, which complements the existing literature. The book is clearly written, and difficult concepts are illustrated by means of good examples. The book is suitable for readers with a solidmathematical background as well as some basic systems and control knowledge. The book should provide a useful reference for researchers working in control theory as well as for Ph.D. students." (Alessandro Astolfi, IEEE Control Systems Magazine, February 2009)

• Department of Electrical Engineering, University of Notre Dame, Notre Dame, U.S.A

  Anthony N. Michel

• Department of Electrical and Computer Engineering, St. Cloud State University, St. Cloud, U.S.A

  Ling Hou

• Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, U.S.A

  Derong Liu

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