Open AccessRelaxed stability conditions for polynomial‐fuzzy‐model‐based control system with membership function information
Author(s) -
Zhao Yanbin,
Lam Hak Keung,
Song Ge,
Yin Xunhe
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.0913
Subject(s) - control theory (sociology) , polynomial , fuzzy control system , stability (learning theory) , fuzzy logic , mathematics , function (biology) , computer science , control (management) , artificial intelligence , machine learning , mathematical analysis , biology , evolutionary biology
This study presents a new approach for stability analysis of polynomial‐fuzzy‐model‐based (PFMB) control system using membership function information. For the purpose of extracting the regional information of the membership functions, the operating domain is partitioned into several sub‐domains. In each sub‐domain, the boundaries of every single membership function overlap term and the numerical relation among all the membership function overlap terms are represented as a group of inequalities. Through the S‐procedure, the regional membership function information is taken into account in the stability analysis to relax the stability conditions. The operating domain partition scheme naturally arises the motivation of constructing the PFMB control system with the sub‐domain fuzzy controllers. Each polynomial fuzzy controller works in its corresponding sub‐domain such that the compensation capability of controller is enhanced. The sum‐of‐squares (SOS) approach is proposed to obtain the stability conditions of the PFMB control system using the Lyapunov stability theory. The PFMB control system studied in this study has the feature that the number of fuzzy rules and the membership function shapes of the polynomial fuzzy controller can be designed independently from the polynomial fuzzy model. To verify the stability analysis result, a numerical example is given to demonstrate the validity of the proposed method.