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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2006

Common polynomial Lyapunov functions for linear switched systems

Résumé

In this paper, we consider linear switched systems. x( t) = A(u( t))x( t), x is an element of R-n, u is an element of U, {Au u is an element of U} compact, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ( UAS). Given a UAS system, it is always possible to build a common polynomial Lyapunov function. 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. A generalization to a class of piecewise-polynomial Lyapunov functions is given.

Dates et versions

hal-02320784 , version 1 (19-10-2019)

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P Mason, U Boscain, Yacine Chitour. Common polynomial Lyapunov functions for linear switched systems. SIAM Journal on Control and Optimization, 2006, 45 (1), pp.226-245. ⟨10.1137/040613147⟩. ⟨hal-02320784⟩
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