Stability of Dynamical Systems-On the Role of Monotonic and Non-Monotonic Lyapunov Functions [Bookshelf

Abstract

The contents of the book are a review of dynamical systems,the principal stability and boundedness results on metric spaces, specialized stability and boundedness results on metric spaces, applications to discrete-event systems, stability results for finite-dimensional dynamical systems, applications to the stability of finite-dimensional dynamical systems, and stability results for infinite-dimensional systems. Each chapter ends with three final sections: Notes and References, Problems, and Bibliography; these sections are welcome additions that provide insights and perspectives beyond the main content of the chapters. This second edition provides more emphasis on the stability of discrete-event and hybrid systems than the first edition [1] (see [2] for an earlier review), and it emphasizes the use of non-monotonic Lyapunov functions, which the authors developed in their recent research publications. In the Preface, the authors motivate the introduction of non-monotonic Lyapunov functions; this generalization is used to derive a general form of Lyapunov stability results. Further, in the case that the Lyapunov functions are monotonic, standard Lyapunov stability results are obtained. In practice, this extension is primarily motivated by discrete event and hybrid dynamical systems. These new features add significant material to the first edition. This new edition of the book 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.