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On quadratic stability of state-dependent planar switching systems

Shorten, R.; King, C.; Wulff, Kai; Mason, O.

Forschungsberichte der Fakultät IV - Elektrotechnik und Informatik / Technische Universität Berlin

In this paper we consider the stability of a class of switched systems. Specifically, we ask the following question. Given a partition of the state space, and a set of linear dynamics, each of which are active in parts of the state space in a manner governed by the partition, does there exist a quadratic Lyapunov function for the resulting system? For planar systems with conic partitions and two dynamics, necessary and sufficient conditions are given for such a Lyapunov function. Examples are given to illustrate our results.