Robust Guaranteed Cost Reliable Control for Uncertain Discrete-Time Linear Systems

This paper deals with the problem of robust guaranteed cost reliable control for a class of uncertain discrete-time linear systems with actuator failures. The parameter uncertainty in the state matrix is assumed to be time-unvarying norm-bounded. The purpose is to design a state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring among the prespecified subset of actuators, the plant remains stable and guarantees an adequate level of a quadratic cost index. A sufficient condition for the existence of guaranteed cost reliable controller is derived. Furthermore, it is showed that a group of linear matrix inequalities provide a parameterized representation of guaranteed cost reliable controllers. Based on that, the design problem of the optimal guaranteed cost reliable controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques. Finally an example is given illustrating the proposed results.