Output-Feedback Control of Interval Type-2 Fuzzy-Model-Based Systems

Abstract

This chapter is concerned with the problems of state and output-feedback control for IT2 fuzzy systems with mismatched membership functions. The IT2 fuzzy model and the IT2 state and output-feedback controllers do not share the same membership functions. A novel performance index, which is expressed as an extended dissipativity performance, is introduced to be a generalization of $H_{\infty }$, $L_{2}{\!}-{\!}L_{\infty }$, passive and dissipativity performances indexes. Firstly, the IT2 T–S fuzzy model and the controllers are constructed by considering the mismatched membership functions. Secondly, on the basis of Lyapunov stability theory, the IT2 fuzzy state and output-feedback controllers are designed respectively to guarantee that the closed-loop system is asymptotically stable with extended dissipativity performance. The existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems.