Open AccessA nonmonotonically decreasing relaxation approach of Lyapunov functions to guaranteed cost control for discrete fuzzy systems
Author(s) -
Chen YingJen,
Tanaka Motoyasu,
Inoue Kohei,
Ohtake Hiroshi,
Tanaka Kazuo,
Guerra Thierry Marie,
Kruszewski Alexandre,
Wang Hua O.
Publication year - 2014
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.2013.1132
Subject(s) - lemma (botany) , lyapunov function , control theory (sociology) , relaxation (psychology) , fuzzy control system , fuzzy logic , mathematics , cost control , control (management) , mathematical optimization , computer science , nonlinear system , artificial intelligence , psychology , social psychology , physics , quantum mechanics , ecology , statistics , poaceae , biology
This study presents a nonmonotonically decreasing relaxation approach of Lyapunov functions to guaranteed cost control for discrete Takagi–Sugeno (T–S) fuzzy systems. First, the authors summarise the previous results on a relaxation of nonmonotonically decreasing of Lyapunov functions, and newly derive one lemma based on the previous results. Based on the newly derived lemma, they propose guaranteed cost control design for discrete T–S fuzzy systems. The design conditions can be represented in terms of linear matrix inequalities and provide more relaxed results than the existing approach. A design example is included to demonstrate the relaxation effectiveness of the proposed approach in guaranteed cost control.