Fuzzy Mixed H2/H? Sampled-Data Control Design for Nonlinear Dynamic Systems

Abstract

This paper is concerned with a fuzzy mixed H₂/H_? sampled-data control problem for nonlinear systems. A continuous-time Takagi-Sugeno (T-S) fuzzy system is constructed to approximate a nonlinear system. Due to the control input is a zero-order hold sampled-data signal, it is equivalent to a piecewise continuous delay. When a zero-order control input is considered, the closed-loop system can be seen as an input delay system. By using the input delay approach and Lyapunov-Krasovskii functional with Leibniz-Newton formula, a new sufficient condition for the existence of fuzzy sampled-data controller is given in terms of linear matrix inequalities (LMIs). Based on the proposed fuzzy mixed H₂/H_? controller, not only the suboptimal H₂control performance can be achieved, but also external disturbance on the regulation error is attenuated to a prescribed level. Two examples are given to illustrate the effectiveness and feasibility of the sampled-data control design.