A General Robustness Theorem for Switched Linear Systems

In this paper, we study the robustness property of switched linear systems under linear perturbations. We prove that, if the normal switched system is asymptotically stabilizable, then the perturbed switched system is also asymptotically stabilizable if the perturbation is sufficiently small. The theorem generates the previous robustness results reported in the literature. Its implication to structural stability of switched control systems is briefly discussed