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

The α-exponential stability analysis and l1 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 l1 gain constraint is also presented while imposing α-exponential stability, upon which, a constrained l1 controller is designed for both single-input and multi-input cases. Finally, an example is given to show the feasibility of the theoretical results.