Robust Reliable Guaranteed Cost Control of Linear Descriptor Time-Delay Systems with Actuator Failures

This paper deals with the problem of robust reliable guaranteed cost control for a class of uncertain linear descriptor time-delay systems with actuator failures. The parameter uncertainty in the state matrix is assumed in fractional form, which contains the popular norm-bounded uncertainty. And the actuator mold adopted in this paper is in complete form to describe variation of the actuator. The purpose is to design a memoryless state feedback controller such that, for admissible uncertainties as well as actuator failures occurring among the prespecified subset of actuators, the plant remains asymptotically stable and guarantees an adequate level of a quadratic cost index. A sufficient condition for the existence of such controller is derived in the form of Lyapunov inequality. Furthermore, it is showed that a group of linear matrix inequalities provides a parameterized representation of robust reliable guaranteed cost controllers. Based on that, the design problem of the optimal robust guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques. Finally, an example provided in this paper show the technical potentional of this method