Exponential stability analysis and L2-gain control synthesis for positive switched T–S fuzzy systems. (February 2018)

• Record Type: Journal Article
• Authors: Li, Shuo; Xiang, Zhengrong
• Is Part Of: Nonlinear analysis. Volume 27(2018)
• Page Start: 77
• Page End: 91
• Publication Date: 2018-02
• Subjects: Positive switched systems -- T–S fuzzy modeling -- Weighted L2-gain performance -- Stabilization -- Piecewise quadratic copositive Lyapunov function; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2017.08.006
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, the problems of exponential stability analysis and weighted L 2 -gain control synthesis for positive switched T–S fuzzy systems are addressed. Firstly, by proposing a piecewise quadratic copositive Lyapunov function, a less conservative stability condition for positive switched T–S fuzzy systems is derived for the first time. Then, sufficient conditions for the positive switched T–S fuzzy system to be exponentially stable with a weighted L 2 -gain performance are obtained. Based on the obtained results, a state-feedback controller by the parallel distributed compensation scheme is designed to stabilize the positive switched T–S fuzzy system, while guaranteeing the prescribed weighted L 2 -gain performance and positivity in closed-loop. Finally, two numerical examples are presented to demonstrate the effectiveness of the obtained theoretical results.