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Reliable \(H_{\infty}\) control for a class of switched nonlinear systems with actuator failures. (English) Zbl 1118.93351

Summary: This paper focuses on the problem of reliable \(H_{\infty }\) control for a class of switched nonlinear systems with actuator failures among a prespecified subset of actuators. We consider the case in which the never failed actuators cannot stabilize the system. The multiple-Lyapunov-function method is exploited to derive a sufficient condition for the switched nonlinear system to be asymptotically stable with \(H_{\infty }-norm\) bound. This condition is given in the form of a set of partial differential inequalities. As a special application, a hybrid state feedback strategy is proposed to solve the standard \(H_{\infty }\) control problem for non-switched nonlinear systems when no single continuous controller is effective.

MSC:

93D20 Asymptotic stability in control theory
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
93D30 Lyapunov and storage functions
93C15 Control/observation systems governed by ordinary differential equations
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