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A new stability analysis of switched systems. (English) Zbl 0953.93015

The authors consider the switched system

x ˙=f i (x),i=1,2,,K,K+1,,K+K ˜

such that for all i the origin is an equilibrium. For i=1,,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:
93B12Variable structure systems
93D05Lyapunov and other classical stabilities of control systems
93B18Linearizability of systems
93D15Stabilization of systems by feedback