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Finite time stability analysis of switched systems with stable and unstable subsystems. (English) Zbl 1300.93126

Summary: In this paper, we study the finite time stability of nonlinear switched systems consisting of both stable and unstable subsystems. First, the finite time stability of systems is studied using the activation time of the subsystems. We show that if the total activation time of unstable subsystems is relatively small compared with that of finite time stable subsystems, then finite time stability of switched systems is guaranteed. Second, the finite time stability of systems is studied based on the comparison principle. We show that if the comparison system is finite time stable, then the finite time stability of switched systems is guaranteed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed methods.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C15 Control/observation systems governed by ordinary differential equations
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