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Finite-time \(H_\infty\) bumpless transfer control for switched systems: a state-dependent switching approach. (English) Zbl 1465.93191

Summary: This paper addresses the finite-time \(H_\infty\) bumpless transfer control problem for switched systems. The main idea lies in designing a state-feedback controller with amplitude limitation and a state-dependent switching law to reduce control bumps caused by switching. First, a local bumpless transfer condition is proposed to limit the amplitude of switching controllers at switching points. Second, by introducing a state-dependent switching law, a prescribed finite-time \(H_\infty\) bumpless transfer control performance is attained even if it does not hold for each subsystem or system state remaining on a switching surface. Third, a sufficient condition verifying the solvability of finite-time \(H_\infty\) bumpless transfer control problem is established by resorting to multiple Lyapunov function method. Finally, the effectiveness of developed method is illustrated by a numerical example.

MSC:

93D40 Finite-time stability
93B36 \(H^\infty\)-control
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B52 Feedback control
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