Controller Design Of Ito Stochastic Fuzzy Systems

In practical life,it is necessary to control the complex nonlinear systems which are difficult to establish accurate mathematical models.Therefore,fuzzy control becomes a powerful tool for analyzing the performance of nonlinear systems.However,due to the insufficiency of the type-1 fuzzy set in dealing with the uncertainties,the proposed type-2 fuzzy set overcomes the deficiency of type-1 fuzzy set,yet it increases the amount of computation.As a special case of the type-2 fuzzy set,the interval type-2 fuzzy set in-herits the advantages of the type-2 fuzzy set and defines the sub-degree of membership as one to simplified operation.Hence,the theory of the interval type-2 fuzzy control is often applied to solve the system problems about stability analysis,controller and filter design.This paper mainly studies the stability analysis and controller design of Ito stochastic fuzzy system based on T-S model.Then,by employing Ito formula,Direct product for-mula and linear matrix inequalities,the above problems are analysed.The main research is as follows:Firstly,the stability analysis and controller design of Ito stochastic system is studied.The slack variables are introduced by the properties of the membership function of inter-val type-2 fuzzy set,and the sufficient conditions for the stochastic asymptotic stability of the systems are more general.The method of the state feedback controller design is proposed.And the feasibility and effectiveness of the proposed method are verified by numerical examples.The second part,focuses on the problem of the stability analysis for Ito stochastic interval type-2 fuzzy system with time-varying delays and parameter uncertainties.By constructing the Lyapunov-Krasovskii functional,the slack variables are introduced by the properties of the membership function of interval type-2 fuzzy set,and the related matrix inequalities are scaled based on the improved Jensen inequality and reciprocal convex combination techniques.A more general sufficient conditions for mean square stability of the systems are proposed.The effectiveness of the proposed method is verified by numerical examples.In the third part,we deal with the controller design problem for the Ito stochastic interval type-2 fuzzy system with time-varying delays and parameter uncertainties.By constructing the Lyapunov-Krasovskii functional,the correlation matrix in the second part of the theorem is transformed,and the sufficient conditions for the systems mean square stability are proposed and the design method of the controller is given.The feasibility of the proposed method is verified by numerical examples.