Switching Law of a Three Second-Order Linear Time Invariant Switched System

In this work, we study a problem of asymptotically stabilizing of a switched system, which consists of second-order linear time invariant subsystems. The subsystems used in this work have complex eigenvalues and two out of three subsystems cannot be stabilized. We then find a third subsystem and a new switching law that makes overall system asymptotically stabilizable. We propose a new sufficient condition on eigenvalues of the 3rd subsystem and a switching law that allows asymptotically stabilizable the overall switched system. A numerical example has been shown to guarantee the effectiveness of the proposed condition.

Keywords: Switched systems; Switching Law; Asymptotic stabilization

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