Design of delay dependent robust H∞ reliable controller for uncertain time varying delay systems against actuator failure

The problem of robust H_infin reliable control is investigated for time-varying delayed uncertain systems against actuator failures. In the considered system, the parameter uncertainty satisfies a generalized matching condition, and the time-varying delay is bounded and its derivative is unbounded. All the outputs of the actuator failures are assumed to be zero. Based on Lyapunov-Razumkhin stability theory, a sufficient condition of the existence of robust reliable controller which enables the closed-loop system to possess H_infin performance index is given. At the same time, a designing approach of memoryless state-feedback controller is presented. The sufficient condition is represented by linear matrix inequalities (LMIs) and has relevance to time delay. The resultant control systems retain asymptotic stability and disturbance attenuation with H_infin -norm bounds irrespective of any outages within a prespecified subset of actuators. A numerical example shows the validity of the proposed design method.