| In 1985,T.Takagi and M.Sugeno first proposed T-S fuzzy model,the general method based on T-S fuzzy model is to use T-S fuzzy model to represent or approximate a nonlinear system.Fuzzy model is described by a series of fuzzy ”IF-THEN” rules,and represents the local linear input and output relations of the system,these local linear models are smoothly integrated by membership functions.Then,we can use the existing linear system theory to analyze and design these nonlinear systems,which has attracted the attention of many scholars.This paper is divided into three chapters,the main contents are as follows:In Chapter 1,we give brief describes the research background and research contents of T-S fuzzy stochastic systems,and summarizes their research status,and then puts forward the main contents of this paper.In Chapter 2,the stability of discrete T-S fuzzy stochastic systems with time-varying delays is studied.The stochastic delay-dependent stability criteria of stochastic T-S fuzzy systems with time-invariant delays and time-varying delays are derived respectively.In the case of time-varying delay,a new fuzzy Lyapunov-Krasovskii functional(LKF)is constructed,which does not require all symmetric matrices involved to be positive definite to reduce conservatism.These stability conditions are expressed by finite linear matrix inequality(LMIs),which can be effectively solved by standard LMIs optimization techniques.The feasibility of this method is illustrated by two examples.In Chapter 3,the dissipative analysis of discrete T-S fuzzy stochastic systems with time-varying delays is studied,and the conditions with lower conservatism are obtained.By constructing a new fuzzy Lyapunov-Krasovskii functional and using discrete Jensen inequality,the condition of stochastic dissipation of the system is obtained.The validity of this method is verified by MATLAB solution,and compared with the existing literature,the method in this paper is less conservative and the computational complexity is reduced. |
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