State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions

• Published in: IEEE transactions on fuzzy systems Vol. 23; no. 6; pp. 1943 - 1957
• Main Authors: Hongyi Li, Xingjian Sun, Ligang Wu, Lam, H. K.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Educational institutions; Extended dissipativity; Feedback control systems; Fuzzy control; Fuzzy logic; Fuzzy systems; Interval type-2 fuzzy system; Lyapunov stability theory; Output feedback; Performance analysis; State feedback; fuzzy control; interval type-2 fuzzy system; Extended dissipativity; Lyapunov stability theory
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2014.2387876

This paper is concerned with the problems of state and output feedback control for interval type-2 (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 ∞ , L 2- L ∞ , passive, and dissipativity performances indexes. First, the IT2 Takagi-Sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions. Second, 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, which can be solved by standard software. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.