Observer-based reliable exponential stabilization and H∞H∞ control for switched systems with faulty actuators: An average dwell time approach

This paper deals with the problem of reliable stabilization and H∞H∞ control for a class of continuous-time switched Lipschitz nonlinear systems with actuator failures. We consider the case that actuators suffer “serious failure”—the never failed actuators cannot stabilize the given system. The differential mean value theorem (DMVT) allows transforming the switched Lipschitz nonlinear systems into switched linear parameter varying (LPV) systems. Based on average dwell time scheme and under the condition that activation time ratio between stabilizable subsystems and unstabilizable ones is not less than a specified constant, sufficient conditions for reliable exponential stabilization of the switched systems are derived by hybrid observer-based output feedback control. The result is also extended to the reliable H∞H∞ control problem.