Stability of Dynamical Systems

The second edition of this textbook  provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems.  For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonic Lyapunov functions.  Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks.

 The authors cover 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 involving monotonic and non-monotonic Lyapunov functions

- Specialization of this stability theory to finite-dimensional dynamical systems

- Specialization of this stability theory to infinite-dimensional dynamical systems

Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this book can be used as a textbook for graduate courses in stability theory of dynamical systems.  It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences.

Review of the First Edition:

“The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems.  [This] is a very interesting book which complements the existing literature. [It] is clearly written, and difficult concepts are illustrated by means of good examples.”

- Alessandro Astolfi, IEEE Control Systems Magazine, February 2009

• Lyapunov stability
• boundedness of motions
• continuous-time dynamical system
• difference equations
• differential equations in Banach spaces
• discontinuous dynamical system
• discrete-time dynamical system
• dynamical system
• equilibrium point
• finite-dimensional dynamical system
• functional differential equations
• infinite-dimensional dynamical system
• invariance theory
• ordinary differential equations
• partial differential equations
• semigroups

“This new edition of the book by Michel, Hou, and Liu provides a scholarly and comprehensive view of Lyapunov stability that should be accessible to mathematically inclined graduate students and to many researchers in the control field. It is a welcome addition to the published literature.” (N. Harris McClamroch, IEEE Control Systems Magazine, Vol. 36 (1), February, 2016)

“This text have provided comprehensive sources for the materials and results on stability theory of all the dynamical systems … . The book also contains numerous problems and suggestions for further study at the end of the main chapters. … book will provide an excellent source of materials for graduate students studying the stability theory of dynamical systems, and for self-study by researchers and practitioners interested in the systems theory of engineering, physics, computer science, chemistry, life science, and economics.” (Olusola Akinyele, Mathematical Reviews, November, 2015)

• Department of Electrical Engineering, University of Notre Dame, Notre Dame, USA

  Anthony N. Michel

• St. Cloud State University Dept. Electrical & Computer Engineering, St. Cloud, USA

  Ling Hou

• Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, USA

  Derong Liu

Anthony N. Michel, PhD, is Professor Emeritus in the College of Engineering at the University of Notre Dame.

Ling Hou, PhD, is Professor in the Department of Electrical and Computer Engineering at St. Cloud State University.

Derong Liu, PhD, is Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Chicago.

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