Research Of Stability Problems Of T-S Fuzzy Systems With Time-delays

At present, nonlinear time-delay system control theory based on T-S model has made some research, but still in the ascendant, and there are many problems to be solved, so T-S fuzzy time-delay systems need further research and development to play a greater role in the field of Nonlinear control. View of this, In this Paper, the stability analyze and control problems of nonlinear time delay systems have been investigated based on T-S fuzzy model.First the piecewise fuzzy robust dissipative controller of T-S system with time delays is designed with the method of piecewise fuzzy Lyapunov function and linear matrix inequality. The proposed controller can guarantee that for all admissible uncertainties, the resultant closed-loop systems are stable and satisfy dissipative performance. The proposed result is less conservative than the approaches with common Lyapunov function.Then, based on fuzzy weighting-dependent Lyapunov-Krasovskii function, we proposes a method of designing a delay-dependent fuzzy controller for discrete-time T-S fuzzy systems with time delays. To derive a less conservative delay-dependent stabilization condition, the method enhances the interactions among the fuzzy weighting functions, where all the decision variables of fuzzy weighting-dependent Lyapunov-Krasovskii function are set to be associated with the fuzzy weighting functions.Finally, the stability problems of a class of nonlinear time delay fuzzy systems are discussed with Lyapunov-Krasovskii functional approach and the thought of free-weigting matrix. In the Lyapunov functional derivative process, through introduce a number of free matrixs appropriately, we get a new delay-dependent stability criterion based on linear matrix inequality, and further give a sufficient condition for the existence of controller.