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		John LETH,Rafael WISNIEWSKI.[en_title][J].Control Theory and Technology,2012,10(2):176~183.[Copy]

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JohnLETH,RafaelWISNIEWSKI
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(Department of Electronic Systems, Automation and Control, Aalborg University)

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Received:June 10, 2010Revised:April 01, 2011

基金项目:This research was supported by the Danish Council for Technology and Innovation.

On formalism and stability of switched systems

John LETH,Rafael WISNIEWSKI

(Department of Electronic Systems, Automation and Control, Aalborg University)

Abstract:

In this paper, we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching. Based on known results from the theory of differential inclusions, we devise a Lyapunov stability theorem suitable for this class of switched systems. With this, we prove a Lyapunov stability theorem for piecewise linear switched systems by means of a concrete class of Lyapunov functions. Contrary to existing results on the subject, the stability theorems in this paper include Filippov (or relaxed) solutions and allow infinite switching in finite time. Finally, we show that for a class of piecewise linear switched systems, the inertia of the system is not sufficient to determine its stability. A number of examples are provided to illustrate the concepts discussed in this paper.

Key words: Switched systems Differential inclusions Stability Inertia Quadratic forms