Exponential stability analysis and l1 synthesis of positive T-S fuzzy systems with time-varying delays. (May 2017)

• Record Type: Journal Article
• Authors: Meng, Min; Lam, James; Feng, Jun-e; Zhao, Xudong; Chen, Xiaoming
• Is Part Of: Nonlinear analysis. Volume 24(2017)
• Page Start: 186
• Page End: 197
• Publication Date: 2017-05
• Subjects: α-exponential stability -- l1 controller synthesis -- Positive systems -- Takagi–Sugeno fuzzy systems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2017.01.003
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: The α -exponential stability analysis and l 1 controller synthesis of positive Takagi–Sugeno fuzzy discrete-time systems with time-varying delays are discussed in this paper. A sufficient condition of α -exponential stability for autonomous positive fuzzy systems is first established by constructing a new Lyapunov–Krasovskii functional, which depends on a given scalar 0 < α < 1 and the bound of time-varying delays. Then, a sufficient condition for controlled systems with l 1 gain constraint is also presented while imposing α -exponential stability, upon which, a constrained l 1 controller is designed for both single-input and multi-input cases. Finally, an example is given to show the feasibility of the theoretical results.