Robust H∞ control of uncertain fuzzy systems under time-varying sampling

Robust H∞ sampled-data control for uncertain fuzzy systems is discussed. In many practical situations, a system is modeled as a continuous-time fuzzy system, while the control input is the zero-order hold, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the H∞ sampled-data control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, H∞ performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using the Leibniz–Newton formula and free-weighting matrix method for fuzzy time-delay systems under the assumption that sampling time is not greater than some prescribed number. Then, a design method for a robust H∞ sampled-data state feedback controller for uncertain fuzzy systems is proposed. Numerical examples are given to illustrate our robust H∞ sampled-data state feedback control design.