Guaranteed Cost Reliable Control with Exponential Stabilization for Uncertain Delay Systems against Actuator Failure

The problem of guaranteed cost reliable control with exponential stabilization is investigated for time-varying delayed uncertain systems against actuator failure. In the considered systems, the parameters uncertainties satisfy generalized matching conditions, and the time-varying delay and its derivative are bounded. All the output of the actuator failures is assumed to be zero. The cost function of the systems is given in terms of integral quadratic function containing index exponent. By means of state variables transformation, the problem of guaranteed cost reliable control with exponential stabilization is reduced to an equivalent problem of guaranteed cost reliable control. Based on Lyapunov stability theory, a sufficient condition for the existence of guaranteed cost reliable controller with exponential stability is derived and transformed to a linear matrix inequalities (LMI). Further, the approach of optimal guaranteed cost reliable control is given for time-varying delayed uncertain systems under the condition of exponential stabilization. The resultant controller then designed enables the closed-loop system to tolerate actuator failures and to retain exponential stability while to possess the performance index of guaranteed cost despite any outages within a prespecified subset of actuators.