Positive real control for uncertain discrete singular systems with state delay

This paper is concerned with the problem of positive real control for uncertain discrete singular systems with state delay. The discrete singular system under consideration involves state time delay and unstructured time-invariant norm-bounded parameter uncertainties in both the state and input matrices. The problem we address is the design of state feedback controllers such that, for all admissible uncertainties, the resulting closed-loop system is regular, causal and stable while the closed-loop transfer function is extended strictly positive real. A sufficient condition for the existence of the desired feedback controllers is given in terms of two LMIs. When these LMIs are feasible, the expected state feedback controller can be easily constructed via convex optimization. An illustrative example is given to demonstrate the applicability of the proposed approach.