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# On guaranteed cost fuzzy control for nonlinear systems with interval time-varying delay

A guaranteed cost fuzzy control for a class of nonlinear time-delay systems has been reported. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds of the time-varying delay are available. And no restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. The nonlinear time-delay systems are approximated by uncertain Takagi-Sugeno (T-S) fuzzy models with interval time-varying delay. Delay-dependent sufficient conditions on the existence of a guaranteed cost fuzzy controller are derived in terms of matrix inequalities. No model transformation is needed and no slack matrix variable is introduced. A non-convex minimisation problem is formulated for finding the least upper bound of guaranteed cost function under matrix inequality constraints. In order to solve this non-convex minimisation problem, a linearisation iterative algorithm is provided to design a controller achieving a suboptimal guaranteed cost for the considered systems. No parameter needs to be selected in advance. A numerical example is also given to show the effectiveness of the proposed design method.