Switched systems that are periodically stable may be unstable (original) (raw)

2002, Proceedings of the Symposium MTNS

Abstract

In this contribution, we prove the existence of switched linear systems that are periodically stable but are not absolutely stable. The switched linear system associated to the finite set of real matrices {Ap : p ∈ P} is given by xt+1 = Aσ(t)xt. ... Starting from the initial state x0, the trajectory associated to the switching function σ : N → P is given by ... We say that a switched linear system is absolutely stable if trajectories associated to arbitrary switching functions converge to the origin, and that it is periodically stable if trajectories associated to periodic switching functions converge ...

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