On the minimal degree of a common Lyapunov function for planar switched systems

Abstract : In this paper, we consider linear switched systems ẋ(t) = A u(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin.
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Conference papers
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Submitted on : Saturday, October 19, 2019 - 4:56:42 PM
Last modification on : Sunday, October 20, 2019 - 1:01:47 AM

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Paolo Mason, Ugo Boscain, Yacine Chitour. On the minimal degree of a common Lyapunov function for planar switched systems. 2004 43rd IEEE Conference on Decision and Control (CDC), Dec 2004, Nassau, Bahamas. pp.2786-2791. ⟨hal-02320845⟩

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