Extended Dissipative Analysis And Control Of T-S Fuzzy System

The research of control theory based on T-S fuzzy model always has been one of the hotspots in the field of control.T-S fuzzy model is composed of nonlinear membership function and several linear subsystems.This excellent model structure makes it possible to study the complex nonlinear system by using the mature linear system theory.In addition,the extended dissipation theory has become an important tool to analyze the control problems of nonlinear systems.By adjusting the free weighting matrix in the extended dissipation performance,H∞ performance,L2-L∞ performance,passive performance and(Q,S,R)-dissipation performance can be analyzed under the unified framework.Therefore,the analysis and research on the extended dissipation performance of T-S fuzzy system has important theoretical value and practical significance.In this paper,the extended dissipative performance of T-S fuzzy system with time-varying delay is analyzed by designing dynamic output feedback controller and sampled-data controller.The specific work is as follows:Firstly,for uncertain T-S fuzzy systems with time-varying delay and randomly occurring gain variations,the problem of non-fragile dynamic output feedback control is studied.The incomplete premise matching model is established which T-S fuzzy model and fuzzy controller with different membership functions.Based on Lyapunov functional theory and integral inequality technique,sufficient conditions are obtained for the closed-loop system to be asymptotically stable and extended dissipation.Then an example is given to show the effectiveness and superiority of the method.Secondly,a non-fragile sampled-data controller is designed,and a sampled asynchronous model is established to make the fuzzy sampled-data controller and the fuzzy system share the premise variables of the fuzzy model.The extended dissipation performance of T-S fuzzy system with time-varying delay and randomly occurring gain variations is analyzed.The Lyapunov function with quadruple integral term is constructed,and the sufficient criterion for the system to satisfy the extended dissipative performance is obtained.The effectiveness of this method is verified by a practical example.Finally,the research of T-S fuzzy system sampled-data control is applied to T-S semiMarkov jump system.The sampled-data controller with actuator fault is designed,and the extended dissipation performance of T-S fuzzy semi Markov jump system with time-varying delay is analyzed.The Lyapunov function related to the sampled interval is constructed.By using convex combination method and Newton-Leibniz formula,the sufficient conditions for the closed-loop system to be stochastic stable and satisfy the extended dissipation performance index are obtained.Then the feasibility and practicability of the theory are verified by a simulation example.