Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach

We study the stability properties of switched systems consisting of both Hu rwitz stable and unstable linear time-invariant subsystems using an average dwell time approach. We propose a class of switching laws so that the enti re switched system is exponentially stable with a desired stability margin. In the switching laws, the average dwell time is required to be sufficient ly large, and the total activation time ratio between Hurwitz stable subsys tems and unstable subsystems is required to be no less than a specified con stant. We also apply the result to perturbed switched systems where nonline ar vanishing or non-vanishing norm-bounded perturbations exist in the subsy stems, and we show quantitatively that, when norms of the perturbations are small, the solutions of the switched systems converge to the origin expone ntially under the same switching laws.