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Stability Analysis of Hybrid Dynamical Systems

Dynamical systems are families of motions that characterize the evolution of processes along time. For finite dimensional systems the motions are defined on finite dimensional spaces while for infinite dimensional systems the state spaces are infinite dimensional. In the vast literature on the stability theory of dynamical systems, time is usually defined on the real line ( continuous - time systems ) or on the integers (discrete - time systems ), and in the case of the former, the motions are usually assumed to be continuous with respect to time. Advances in technology have given rise to increasingly complex dynamical systems. In many such cases, various components of the motions of dynamical systems evolve simultaneously along different notions of time, including continuous - time, discrete -time, discrete events, and other notions of "time". Such systems, which are of great current interest in a variety of disciplines (including circuits and systems, control theory, mechanics, and the like ) are called hybrid dynamical systems. To date, the vast majority of qualitative studies of such systems has involved specialized models and procedures designed to fit a given problem on hand, with the result that a general qualitative theory of hybrid dynamical systems has been slow in making. In the present lecture we first develop a general model for hybrid dynamical system which is suitable in the stability analysis of such systems. This model, which is applicable to finite as well as to infinite dimensional systems, incorporates a notion of "generalized time". Next, we present Lyapunov and Lagrange stability results for such hybrid dynamical systems. By means of several specific examples, we demonstrate the applicability of our results in a variety of disciplines.

Type of Seminar:
Public Seminar
Prof. Anthony N. Michel
Department of Electrical Engineering University of Notre Dame Notre Dame, Indiana,USA
Jun 07, 2000   17:15

ETH Zentrum, ETZ E6, Gloriastrasse 35, 8006 Zurich
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Anthony N. MICHEL has a Ph.D. degree in electrical engineering (Marquette University) and a D.Sc. degree in applied mathematics (Technische Universitaet Graz). He has spent seven years in the aerospace industry and thirty years in academia (Iowa State University and University of Notre Dame). He was chair of the Department of Electrical Engineering for four years and dean of the College of Engineering for ten years at Notre Dame. He is currently the Frank M. Freimann Professor of Engineering at Notre Dame. He is the author or coauthor of six books. His principal interests are in qualitative theory of dynamical systems with applications in control, neural networks, and the like.