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We study the stability properties of switched systems consisting of both Hurwitz stable and unstable linear time-invariant subsystems using an average dwell time approach. We propose a class of switching laws so that the entire switched system is exponentially stable with a desired stability margin. In the switching laws, the average dwell time is required to be suYciently large, and the total activation time ratio between Hurwitz stable subsystems and unstable subsystems is required to be no less than a speci® ed constant. We also apply the result to perturbed switched systems where nonlinear vanishing or non-vanishing norm-bounde d perturbations exist in the subsystems, and we show quantitatively that, when norms of the perturbations are small, the solutions of the switched systems converge to the origin exponentially under the same switching laws.

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