vbid/9783319152752

Description

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 2009Typham this is the title: Stability of Dynamical Systems On the Role of Monotonic and Non-Monotonic Lyapunov Functions 2nd Edition