Stability and stabilization for uncertain fuzzy system with sampled-data control and state quantization

Abstract

This paper studies the stability and stabilization problems of the T-S fuzzy systems with uncertainty and state quantization. Considering that fuzzy membership functions(FMFs) are the main characteristic of T-S fuzzy model, if the information about the membership function is not added, it will be conservative. So, a novel Lyapunov-Krasovskii functional (LKF) which contains not only integral variables but also FMFs is constructed. To include more information about the sampling pattern, the states on both sides of the sampling interval are incorporated into the LKF. When taking the derivative of the LKF, the product terms which consist of derivative of FMFs and LKF coefficient are involved. Then, the product terms are discussed to ensure their negative definition. By further derivation, enough stability conditions are expressed in the form of linear matrix inequalities (LMIs). The sampling intervals and controller parameters for the T-S fuzzy system can be solved by MATLAB toolbox with the optimal parameters. Finally, two numerical examples are simulated to illustrate the effectiveness of the proposed method.