Stabilization Of Interval Type-2 Single Wiener Process Stochastic Fuzzy Systems

Since the theory of fuzzy sets was proposed,processing modeling and complex non-linear control systems have been introduced with a large degree of freedom.On the basis of fuzzy set theory,the T-S fuzzy dynamic model is described by a certain relationship which represents the local linear input-the output of the fuzzy IF-THEN rule to represent the nonlinear system.The controller of the system is designed based on this model.The original type-1 fuzzy sets can not better deal with the uncertainty in academic research,so which gives the birth to the type-2 fuzzy system.Based on the T-S model,this pa-per mainly studies the stability analysis of random fuzzy systems and the problem of the design of its controller.The main research results of this paper are as follows:In the first part,we deal with the stability analysis and stabilization problem for inter-val type-2 stochastic fuzzy systems with parameter uncertainty and random characteris-tics.The uncertainty is assumed to be a linear fractional form.By employing a Lyapunov function approach,a matrix decomposition technique,a matrix inequality scaling tech-nique as well as the Schur complement lemma,the state feedback controller is developed based on the parallel distribution compensation method.Then,sufficient conditions for ensuring the asymptotic stability of the interval type-2 stochastic fuzzy systems are es-tablished.Finally,the effectiveness of the proposed results is illustated via a simulation example.The second part is considered with the interval type-2 stochastic fuzzy systems with time-varying delays.The improved Jensen inequality combined with reciprocal convex combination lemma are proposed to analyse the asymptotic stability problem of the in-terval type-2 stochastic delayed fuzzy systems.By constructing Lyapunov-Krasovskii functional,a less conservative stabilization condition based on linear matrix inequality method is thus established for the underlying systems.The third part focuses on the problem of the controller design for the interval type-2 stochastic delayed fuzzy systems.Based on the established conditions in the second part,the method of making the closed-loop system mean square stable is presented by using matrix variable substitution approach.Numerical examples are given and a feasible solution is solved with the LMI toolbox in Matlab.The gain matrices of the controller which make the underlying system mean square stable are obtained.