Open AccessMembership‐dependent stability analysis of discrete‐time positive polynomial fuzzy‐model‐based control systems with time delay
Author(s) -
Bao Zhiyong,
Mehran Kamyar,
Lam Hak Keung,
Li Xiaomiao
Publication year - 2020
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.2019.0723
Subject(s) - control theory (sociology) , mathematics , fuzzy control system , membership function , polynomial , fuzzy logic , fuzzy number , stability (learning theory) , boundary (topology) , controller (irrigation) , mathematical optimization , fuzzy set , computer science , control (management) , artificial intelligence , mathematical analysis , machine learning , agronomy , biology
This study proposes a novel, relaxed, Lyapunov‐based and membership‐function dependent stabilisation analysis of discrete‐time polynomial‐fuzzy‐model‐based (PFMB) control systems with time delay under positivity constraint. The discrete‐time non‐linear system with time delay is represented by a polynomial fuzzy model, and corresponding PFMB controller is designed using imperfect premise matching technique which does not require its fuzzy rule and shape of membership functions be matched with those of the model. The authors take advantage of this property to relax the conservativeness of the obtained stability results by introducing the information of membership functions, i.e. the relationship constraint information of membership functions between the model and the controller and boundary information of membership functions, into the stability and positivity conditions. A numerical example is given to demonstrate the effectiveness of the proposed approach.