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Dynamic output stabilizing design for discrete-time fuzzy systems with time-varying delay

The design of a distributed-compensation (DC) output feedback controller for discrete-time fuzzy systems with time-varying delay is proposed by the formulation of convex optimization problems, formulated as a set of linear matrix inequalities (LMIs). At the exception of controller matrix D, all other are designed depending on the the submodes of the fuzzy system and assembled together by fuzzy inference rules. The novelty of this proposal is that the controller is composed by a classical part, feeding-back the system output, and another where the delayed output of the system is dynamically feedback, whenever the delay is known. Different from other approaches found in the literature, it is used a parameter dependent Lyapunov-Krasovskii function candidate and extra matrices to reduce the conservatism of the proposed approach. Numerical experiments are presented showing the effectiveness of the proposal.