Observer-Based Fuzzy l 2 –l ∞ Control for Discrete-Time Nonlinear Systems
Xiao‐Heng Chang, Xu Han · IEEE Transactions on Fuzzy Systems · 2023
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.