Relaxed stability conditions for polynomial-fuzzy-model-based control system with membership function information

TY - JOUR

T1 - Relaxed stability conditions for polynomial-fuzzy-model-based control system with membership function information

AU - Zhao, Yanbin

AU - Lam, Hak Keung

AU - Song, Ge

AU - Yin, Xunhe

PY - 2017/4/6

Y1 - 2017/4/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85020417897&partnerID=8YFLogxK

U2 - 10.1049/iet-cta.2016.0913

DO - 10.1049/iet-cta.2016.0913

M3 - Article

AN - SCOPUS:85020417897

SN - 1751-8644

VL - 11

SP - 1493

EP - 1503

JO - Iet Control Theory And Applications

JF - Iet Control Theory And Applications

IS - 10

ER -