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Density and flow: A different view on nonlinear control

The concept of "density functions" has recently been introduced as a tool for stability analysis of nonlinear ordinary differential equations. Statements are given in terms of "almost all trajectories" of the system. The theory is similar to the classical theory of Lyapunov, but the implications are weaker and applicable to many situations where global stability in the classical sense does not hold. Density functions also have remarkably nice properties for control synthesis. While the set of control Lyapunov functions for a given system may not even be connected, the corresponding set for density functions is always convex. This opens new possibilities for nonlinear control synthesis by convex optimization. In this seminar we discuss the duality between density functions and Lyapunov functions and a converse theorem that proves existence of a density function from assumptions on almost global stability. Simple examples of pendulum dynamics turn out to be illuminating.

Type of Seminar:
Public Seminar
Prof. Anders Rantzer
Dept. of Automatic Control, Lund Institute of Technology,Box 118 S-22100 Lund
Oct 28, 2002   11:00

ETH Zentrum, Gloriastr. 35, 8006 Zurich, Building ETZ, Room F76.1
Contact Person:

Prof. P. Parrilo
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Biographical Sketch:
Anders Rantzer was born in 1963. He received a Ph.D. degree in optimization and systems theory from the Royal Institute of Technology (KTH), Stockholm, Sweden. After postdoctoral positions at KTH and at IMA, University of Minnesota, he joined the Department of Automatic Control, Lund, in 1993. In 1999, he was appointed as professor of Automatic Control. Prof. Rantzer was a winner of the 1990 SIAM Student Paper Competition and 1996 IFAC Congress Young Author Price. He is a Fellow of IEEE and has served as associate editor of IEEE Transactions on Automatic Control and several other journals. His research interests are in modeling, analysis and synthesis of control systems, with particular attention to uncertainty, nonlinearities and hybrid phenomena.