Membership-function-dependent dynamic output feedback H∞ controller design of continuous-time T-S fuzzy systems via non-quadratic Lyapunov function

Jian Zhang; Xianghua Wang; Youqing Wang

doi:10.1016/j.isatra.2022.09.006

Membership-function-dependent dynamic output feedback H_∞ controller design of continuous-time T-S fuzzy systems via non-quadratic Lyapunov function

ISA Trans. 2023 Mar:134:212-225. doi: 10.1016/j.isatra.2022.09.006. Epub 2022 Sep 13.

Authors

Jian Zhang¹, Xianghua Wang¹, Youqing Wang²

Affiliations

¹ College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China.
² College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, China. Electronic address: wang.youqing@ieee.org.

PMID: 36163197
DOI: 10.1016/j.isatra.2022.09.006

Abstract

The dynamic output feedback H_∞ (DOFH) control under imperfect premise matching (IPM) is studied in this paper for continuous-time Takagi-Sugeno (T-S) fuzzy systems. Different from the existing results, the DOFH switching controller, which enjoys membership functions (MFs) distinct from the fuzzy systems, is designed. First, the non-quadratic Lyapunov function (NQLF) based on MFs is utilized to design the controller. The time derivatives of MFs are addressed by the switching strategy. Second, a method based on linear matrix inequality (LMI) is given to make the controller gains solvable. Third, an improved method is developed to incorporate the more boundary information of MFs into the stability conditions to reduce conservatism. Finally, three examples are used to certify the advantage of the approach.

Keywords: Dynamic output feedback control; Imperfect premise matching; Membership-function-dependent; Non-quadratic Lyapunov function; T–S fuzzy systems.