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A geometry-based algorithm for the stability of planar switching systems

This paper describes a geometric procedure, whose aim is to provide necessary and sufficient conditions for the stability of a class of planar switching systems against arbitrary switching. The main idea is to build the worst switching sequence and to exploit it to get information about the stability for every switching sequence. The analysis is conveyed initially for LTI subsystems, then it is extended to homogeneous subsystems of the same degree having the origin as the unique equilibrium point. Finally, a simple method to build suitable Lyapunov functions to verify the stability of such systems is provided.