Reliable control for a class of switched nonlinear systems with actuator failures

This paper focuses on the problem of reliable H ∞ 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 ∞ -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 ∞ control problem for non-switched nonlinear systems when no single continuous controller is effective.