Finite-time stability and stabilization of interval type-2 fuzzy systems with time delay

Article type: Research Article

Authors: Dian, Songyi | Liang, Weibo | Zhao, Tao^{; *}

Affiliations: College of Electrical Engineering and Information Technology, Sichuan University, Chengdu, China

Correspondence: [*] Corresponding author. Tao Zhao, College of Electrical Engineering and Information Technology, Sichuan University, Chengdu 610065, China. Tel.: +86 02885466818; E-mail: zhaotaozhaogang@scu.edu.cn.

Abstract: Finite-time stability and stabilization problems for a class of interval type-2 (IT2) fuzzy time-delay systems are studied. In this paper, we extend the concept of finite-time stability to IT2 fuzzy time-delay systems. Based on the Lyapunov stability method, integral inequality and some advanced matrix inequalities, a sufficient condition is proposed to guarantee finite-time stability of IT2 fuzzy time-delay systems. Then, by virtue of the results on finite-time stability and Finsler’s lemma, we propose an IT2 fuzzy state feedback controller which can guarantee the closed-loop system is finite time stable. The problem of finite time stabilization can be solved with con complementarity linearization iterative algorithm. Finally, two numerical examples are provided to verify the effectiveness of the proposed approach.

Keywords: IT2 fuzzy systems, state feedback control, finite-time, time-delay

DOI: 10.3233/JIFS-18933

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 6, pp. 6537-6549, 2018