Fuzzy control of delayed systems: Less conservative convex conditions

Convex conditions for stability analysis and control synthesis for discrete-time fuzzy systems with delayed state are proposed in this paper. The conditions are obtained by considering a parameter dependent Lyapunov-Krasovskii functional, slack matrix variables and, in the synthesis case, an instrumental variable. In all cases, the conditions are formulated as an LMI (linear matrix inequality) feasibility test, that can be efficiently solved in polynomial time by specialized numerical solvers. It is shown that the proposed conditions encompass quadratic stability based formulations. Moreover, in the stability analysis case, conditions published recently in the literature can be recovered as a particular case from those proposed in this paper. Convex conditions for controller synthesis are proposed using an instrumental variable, yielding complementary results when compared with other conditions recently published in the literature. Numerical examples are presented to illustrate the efficiency of the proposed conditions. Comparisons are made with other conditions from the literature.