A nonmonotonically decreasing relaxation approach of Lyapunov functions to guaranteed cost control for discrete fuzzy systems. Issue 16 (1st November 2014)

• Record Type: Journal Article
• Authors: Chen, Ying‐Jen; Tanaka, Motoyasu; Inoue, Kohei; Ohtake, Hiroshi; Tanaka, Kazuo; Guerra, Thierry Marie; Kruszewski, Alexandre; Wang, Hua O.
• Is Part Of: IET control theory & applications. Volume 8:Issue 16(2014)
• Page Start: 1716
• Page End: 1722
• Publication Date: 2014-11-01
• Subjects: Lyapunov methods -- discrete systems -- fuzzy systems -- control system synthesis -- fuzzy control -- linear matrix inequalities -- relaxation theory; nonmonotonically decreasing relaxation approach -- Lyapunov functions -- discrete fuzzy systems -- discrete Takagi–Sugeno fuzzy systems -- discrete T–S fuzzy systems -- guaranteed cost control design -- linear matrix inequalities; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2013.1132
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : 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.