Stabilization of Second-Order LTI Switched Systems

Xuping Xu, P.J. Antsaklis, K.X. He, and M.D. Lemmon

Proceedings of the 1999 Conference on Decision and Control
pp. 1339-1344. Phoenix, AZ, USA, December 7-10, 1999.

Abstract- In this paper, the problem of asymptotically stabilizing switched systems consisting of second-order LTI subsystems is studied and solved. In a previous paper, the stabilization problem of switched systems consisting of subsystems with unstable foci was addressed. This paper extends the method therein to the stabilization of switched systems consisting of general second-order LTI subsystems. Necessary and sufficient conditions for stabilizability for such systems are obtained. Stabilizing switching control laws are also derived if the system is asymptotically stabilizable. Examples throughout the
paper illustrate the approach and results.

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