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An important class of hybrid dynamical systems are switched systems which include multimodal systems or systems with variable structure. In the present paper we build on our earlier work on qualitative theory of discontinuous dynamical systems to establish new results for the stability and asymptotic stability of an equilibrium of such systems (defined on finite dimensional spaces). The results presented herein are less conservative than existing stability results for switched systems.
Hou et al. (Tue,) studied this question.