Abstract
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.
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