Observer-Based Fuzzy l 2–l∞ Control for Discrete-Time Nonlinear Systems

In this article, an observer-based $l_{2}$ – $l_\infty$ performance analysis and controller design problem is proposed for a category of discrete-time nonlinear control systems. First of all, the closed-loop system with external disturbance in both state and output variables under consideration is represented as a discrete-time Takagi–Sugeno (T–S) fuzzy model and is described by the descriptor representation method. Subsequently, a new Lyapunov function is suggested that satisfies the prescribed $l_{2}$ – $l_\infty$ performance while ensuring stability. The application of the linear matrix inequality technique is employed to establish an analysis criterion for the $l_{2}$ – $l_\infty$ performance. By defining the structure of matrix variables, new design conditions of observer-based $l_{2}$ – $l_\infty$ controller are given. Ultimately, an instance demonstrates the effectiveness of the proposed controller design criterion.