Einladung zum Vortrag im Kolloquium Technische Kybernetik
Dissipative Dynamical Systems
Prof. Jan C. Willems
Department of Electrical Engineering
Katholieke Universiteit Leuven, Leuven, Belgium
Zeit: Mittwoch · 29. 11. 2006 · 11:30 Uhr
Ort: Hörsaal 9.01 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen
Abstract
The notion of a dissipative system was introduced in the early 1970’s. It generalizes the idea of a
Lyapunov function to ‘open’ dynamical systems. This concept has found applications in diverse areas
of systems and control, for example, in stability theory, system norm estimation, and robust control. A
central problem that emerges is the construction of a storage function. It is this problem that brought
LMI’s to the foreground.
The aim of this talk is to show how dissipativity is formalized as a mathematical concept, and discuss
a number of applications and recent generalizations. A dissipative system is defined in terms of a supply
rate, a storage function, and the dissipation inequality. The construction of storage functions in the case of
linear systems with quadratic supply rates leads to the synthesis of impedances by means of passive electrical
circuits. Storage functions are also instrumental for establishing stability criteria for interconnected
systems. For PDE’s, the dissipation inequality involves both a storage and a flux. Their construction in
the linear quadratic case leads to the factorization of polynomial matrices in many variables and Hilbert’s
17-th problem regarding the sum-of-squares representation of nonnegative polynomials in many variables.
The relevance of these results will be illustrated by Maxwell’s equations.
Biographical Information
Prof. Jan C. Willems studied engineering at the University of Ghent. After graduation in 1963, he worked towards a PhD degree in electrical engineering at the Massachusetts Institute of Technology that he obtained in 1968. He was an assistant professor there from 1968 to 1973. In 1973, he was appointed Professor of Systems and Control in the Mathematics department of the University of Groningen. He became emeritus in 2003. Since 2003, he has been a Guest Professor at the department of electrical engineering of the Katholieke Universiteit Leuven in Belgium.
Prof. Willems has been one of the greatest contributors to the field of automatic control over the past 40 years. Early in his career he made seminal contributions to the study of dissipativity that still form the basics for many modern developments. He introduced the highly fruitful concept of "almost invariance" in geometric control theory, and he is the father of the behavioral approach to systems and control. Prof. Willems received may awards and honors, including the IEEE Control System Award, he is founding editor of the Systems and Control Letters, and is a highly influential teacher as well as a gifted educator. Many of the famous control professors of today obtained their PhD under the supervision of Jan C. Willems. More details are given on http://homes.esat.kuleuven.be/~jwillems/webpage.html
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