Qualitative Theory Of Hybrid Dynamical Systems

The emerging area of hybrid dynamical systems lies at the interface of control theory and computer science, i.e., analogue 'and' digital aspects of systems. This new monograph presents state-of-the-art concepts, methods and tools for analyzing and describing hybrid dynamical systems.

"Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions. Applies the general theory to specific classes of equations. Presents new and expanded material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics."

"Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions. Applies the general theory to specific classes of equations. Presents new and expanded material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics."

This book is primarily a research monograph that presents in a unified man ner some recent research on a class of hybrid dynamical systems (HDS). The book is intended both for researchers and advanced postgraduate stu dents working in the areas of control engineering, theoretical computer science, or applied mathematics and with an interest in the emerging field of hybrid dynamical systems. The book assumes competence in the basic mathematical techniques of modern control theory. The material presented in this book derives from a period of fruitful research collaboration between the authors that began in 1994 and is still ongoing. Some of the material contained herein has appeared as isolated results in journal papers and conference proceedings. This work presents this material in an integrated and coherent manner and also presents many new results. Much of the material arose from joint work with students and colleagues, and the authors wish to acknowledge the major contributions made by Ian Petersen, Efstratios Skafidas, Valery Ugrinovskii, David Cook, Iven Mareels, and Bill Moran. There is currently no precise definition of a hybrid dynamical system; however, in broad terms it is a dynamical system that involves a mixture of discrete-valued and continuous-valued variables. Since the early 1990s, a bewildering array of results have appeared under the umbrella of HDS, ranging from the analysis of elementary on-off control systems to sophis ticated mathematical logic-based descriptions of large real-time software systems.

This book deals with the global qualitative behavior of flows and diffeomorphisms. It presents a systematic study of the fundamental theory and method of dynamical systems, from local behavior near a critical (fixed) point or periodic orbit to the global, such as global structural stability, bifurcations and chaos. It emphasizes the global non-hyperbolicity and introduces some new results obtained by Chinese mathematicians which may not be widely known. Contents:Preparations of Differentiable Manifolds and Differential TopologyDynamical Systems on ManifoldsLocal Properties of Flows and DiffeomophismsStructural Stability and BifurcationsChaotic BehaviorGeneric Properties Readership: Pure and applied mathematicians and applied scientists. keywords: “… a clear and easy-to-read introduction to dynamical systems in which one can find many definitions, much information and also some important proofs.” Mathematical Reviews “The style of the book is brief and compact, and the selected materials are lucid and refined. Each topic is stated clearly from the simple to the profound. This book can serve both as an easy-reading introduction to the study field of dynamical systems for the beginner and as a valuable reference for the specialists.” Mathematics Abstracts

This book constitutes the refereed proceedings of the Third International Workshop on Hybrid Systems: Computation and Control, HSCC 2000, held in Pittsburgh, PA, USA in March 2000.; The 32 revised full papers presented together with abstracts of four invited talks were carefully reviewed and selected from a total of 71 papers submitted.; The focus of the works presented is on modeling, control, synthesis, design and verification of hybrid systems.; Among the application areas covered are control of electromechanical systems, air traffic control, control of automated freeways, and chemical process control.

It is with great pleasure that I offer my reflections on Professor Anthony N. Michel's retirement from the University of Notre Dame. I have known Tony since 1984 when he joined the University of Notre Dame's faculty as Chair of the Depart ment of Electrical Engineering. Tony has had a long and outstanding career. As a researcher, he has made im portant contributions in several areas of systems theory and control theory, espe cially stability analysis of large-scale dynamical systems. The numerous awards he received from the professional societies, particularly the Institute of Electrical and Electronics Engineers (IEEE), are a testament to his accomplishments in research. He received the IEEE Control Systems Society's Best Transactions Paper Award (1978), and the IEEE Circuits and Systems Society's Guillemin-Cauer Prize Paper Award (1984) and Myril B. Reed Outstanding Paper Award (1993), among others. In addition, he was a Fulbright Scholar (1992) and received the Alexander von Hum boldt Forschungspreis (Alexander von Humboldt Research Award for Senior U.S. Scientists) from the German government (1997). To date, he has written eight books and published over 150 archival journal papers. Tony is also an effective administrator who inspires high academic standards.