Analysis And Design For T-S Model Based Interval Type-2Stochastic Fuzzy Systems

This paper presents the problems of the stability analysis and controller design for interval type-2Ito stochastic fuzzy systems. The superiority of interval type-2fuzzy sets over type-1fuzzy sets isthat it can handle the uncertainties directly. The main content of the research includes the followingthree parts:The first part focuses on the problems of stability of interval type-2Ito stochastic fuzzy systems.Sufficiency conditions of stability for the systems are derived by using a Lyapunov-based approach.To facilitate the stability analysis, the information of the footprint of uncertainty is used to developsome membership function conditions,which allow the introduction of slack matrices to derive aless conservative result. Finally, two simulation examples have proved the merits and validity of theproposed method.Part2, we discuss the problems of controller design of uncertain interval type-2Ito stochasticfuzzy systems with multidimensional Wiener process. The uncertainty of the system is with thelinear fractional type. Sufficiency conditions of stability for the systems are established by using aLyapunov-based approach. Finally, a vivid example has proved the validity of our results.Part3, we consider the problems of stability of interval type-2stochastic fuzzy systems withtime delay. Lyapunov-Krasovskii functional is obtained by using delay decomposition approach.Based on Lyapunov stability theory and Jensen inequality techniques, a new delay-dependentcriterion is obtained. Finally, a vivid example has proved the validity of our results.