Design of Stabilizing Control Laws for Second-Order Switched Systems
X. Xu and P. J. Antsaklis
Abstract -- In this paper, we design asymptotically stabilizing control laws for switched systems consisting of several second-order LTI subsystems with unstable foci. Switching is needed for the stabilization of a system consisting of several subsystems if each of its subsystems is unstable. We first study switched systems consisging of two subsystems with unstable foci and conic switching stabilizing control laws are derived. Then the result is extended to several subsystems. In particular, necessary and sufficient conditions for the asymptotic stabilizability of a switched system are derived. If the switched system is asymptotically stabilizable, an asymptotically stabilizing switching law can also be obtained. Finally, we briefly compare the method derived here to a matrix inequality based design method.
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