Relaxed stability conditions for the Takagi–Sugeno fuzzy system using a polynomial non‐quadratic Lyapunov function. Issue 13 (1st August 2016)

• Record Type: Journal Article
• Authors: Sol Kim, Han; Bae Park, Jin; Hoon Joo, Young
• Is Part Of: IET control theory & applications. Volume 10:Issue 13(2016)
• Page Start: 1590
• Page End: 1599
• Publication Date: 2016-08-01
• Subjects: stability -- fuzzy systems -- polynomials -- Lyapunov methods -- continuous time systems; sum‐of‐squares‐based relaxed stability conditions -- continuous‐time Takagi‐Sugeno fuzzy system -- polynomial nonquadratic Lyapunov function -- SOS‐based relaxed stability conditions -- continuous‐time T‐S fuzzy system -- PNQLF -- fuzzy weighting functions; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2015.1273
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : In this study, sum‐of‐squares (SOS)‐based relaxed stability conditions for the continuous‐time Takagi–Sugeno (T–S) fuzzy system are derived using a polynomial non‐quadratic Lyapunov function (PNQLF). The proposed methods consist of two approaches. Like the previous studies, the first uses the upper bounds on a time derivative of the fuzzy weighting function (TDFWF), and the other directly uses the TDFWF in order to obtain relaxed results and enlarge the domain of attraction. Moreover, unlike the conventional non‐quadratic Lyapunov function, the newly proposed PNQLF uses different fuzzy weighting functions from those of the system in order to solve the existing problems. Finally, the effectiveness of the proposed methods is demonstrated by some numerical examples.