Exponential stability analysis and l1 synthesis of positive T-S fuzzy systems with time-varying delays

The alpha-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 alpha-exponential stability for autonomous positive fuzzy systems is first established by constructing a new Lyapunov-Krasovskii functional, which depends on a given scalar 0 < alpha < 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 a-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. (C) 2017 Elsevier Ltd. All rights reserved.