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An LMI approach to positive real control for discrete time-delay systems

This paper focuses on the problem of positive real control for discrete time-delay systems. The problem we address is the design of a dynamic output feedback controller, which guarantees the asymptotic stability of the closed-loop system and achieves the extended strictly positive realness of a certain closed-loop transfer function. Then, a condition for extended strictly positive realness for discrete-delay systems is developed. Based on this, a sufficient condition for the existence of the desired controllers is proposed in terms of three linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit parametrization of the desired output feedback controller is presented. An illustrative example is given to demonstrate the applicability of the proposed approach.