A novel polynomial membership functions based control method for T-S fuzzy systems

Wen-Bo Xie; Jian Zhang; Yi-Fan Li; Reinaldo M Palhares

doi:10.1016/j.isatra.2022.02.021

A novel polynomial membership functions based control method for T-S fuzzy systems

ISA Trans. 2022 Oct;129(Pt B):192-203. doi: 10.1016/j.isatra.2022.02.021. Epub 2022 Feb 17.

Authors

Wen-Bo Xie¹, Jian Zhang², Yi-Fan Li³, Reinaldo M Palhares⁴

Affiliations

¹ School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China; College of Automation, Harbin University of Science and Technology, Harbin, 150080, PR China.
² College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, PR China. Electronic address: antonia0424@163.com.
³ College of Automation, Harbin University of Science and Technology, Harbin, 150080, PR China.
⁴ Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos, 6627, 31270-010, Belo Horizonte, MG, Brazil.

PMID: 35221091
DOI: 10.1016/j.isatra.2022.02.021

Abstract

To solve the state feedback stabilization problem for a class of T-S fuzzy systems, a new stability synthesis method is raised to further relax the conservatism existing in the analysis process. First, a series of nonlinear polynomials are used to approximate the system membership functions. And satisfied approximation results can be obtained. Then a polynomials transformation method is raised to change the polynomial membership functions into linear form. This method can facilitate the synthesis process and achieve better approximation precision. Therefore, by a membership function involving stability analysis approach, linear matrix inequality form stability conditions are given. Finally, by presenting and analyzing a numerical and a practical examples, the conservatism reduction effects of the proposed methods are verified.

Keywords: Conservatism reduction; Membership function; Polynomial approximation; T–S fuzzy systems.