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A new stability analysis of switched systems. (English) Zbl 0953.93015
The authors consider the switched system $$\dot x=f_i(x), \quad i=1,2,\dots,K,K+1, \dots, K+\widetilde K$$ such that for all $i$ the origin is an equilibrium. For $i=1, \dots,K$ the systems linearized around the origin are exponentially stable. It is shown that for certain sequences of commutations the resulting trajectories are such that the origin of the resulting (overall) system is asymptotically stable.

##### MSC:
 93B12 Variable structure systems 93D05 Lyapunov and other classical stabilities of control systems 93B18 Linearizability of systems 93D15 Stabilization of systems by feedback
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##### References:
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