Uniqueness of limiting solutions with application to switched systems

This paper concerns the uniqueness of limiting solutions w.r.t. a family of differential equations. As in the case of one single differential equation, we show that the uniqueness result can be obtained under a local Lipschitz condition. Such a result is used to establish a necessary condition for uniform global asymptotic stability (UGAS) of switched systems. Particularly, it is shown that the origin of a well-studied switched system is UGAS w.r.t. a family Θ of switching signals if and only if Θ satisfies a persistent excitation condition. This shows the usefulness of the proposed result.

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