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Stability analysis and design of hybrid systems using piecewise quadratic Lyapunov functions

Switched and hybrid systems contain dynamics that is both continuous and discrete (logical-valued) in its nature. The interest in such systems has increased considerably during recent years for several reasons. When the complexity of the technical systems increases, it is not longer possible to suppress the hybrid nature of the systems, and the analysis and design has to be carried out for the interacting continuous and discrete event systems. Another reason is the use and advance of computers as controlling devices. Today, even the simplest devices are controlled by computer programs. It is often natural to invoke controllers that operate during different phases or modes of system cycles. The changes of these modes are usually based on different logical conditions, naturally leading to interacting systems with continuous and logical behavior. In this seminar, the focus is on stability analysis and design of switched and hybrid systems using piecewise quadratic Lyapunov functions. The use piecewise quadratic Lyapunov functions is less conservative than using a single quadratic Lyapunov function, and in some cases even necessary to succeed analysing or designing a hybrid system. Stability conditions, in form of linear matrix inequalities, and design conditions are introduced in the seminar. Furthermore, initial results regarding the state estimation problem will be given. Several examples are introduced to motivate and illustrate the results.
Type of Seminar:
Public Seminar
Prof. Stefan Pettersson
Control and Automation Lab, Chalmers Univ. of Technology, S-412 96 Gothenburg, Sweden
Nov 26, 2004   16:30

ETH Zentrum, Physikstrasse 3, Zurich, Building ETL, Room K 25
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Stefan Pettersson received his M.Sc. in Automation Engineering and Ph.D. in Control Engineering at Chalmers University of Technology, Sweden, in 1993 and 1999 respectively. Currently, he is an Assistant Professor at the Department of Signals and Systems, Control and Automation Lab at Chalmers. The main interest of Stefan's research has been in switched and hybrid systems, and his Ph.D thesis was focused on stability properties for such systems. Inspired by vehicle applications, Stefan's attention has lately been focused on the state estimation problem for hybrid systems. A detailed description of Stefan's CV can be found at: