H∞ control for fuzzy sampled-data systems with discrete and distributed delays

Abstract

This paper discusses an H∞ sampled-data control design for fuzzy systems with discrete and distributed delays. The size of discrete delay and distributed delay is assumed to be not always the same. The zero-order control input can be represented as a delayed input. Then, the closed-loop system with such an input becomes a system with time-varying delay. Sufficient conditions for the closed-loop system to be stable with satisfying a prescribed H∞ performance index are given in terms of linear matrix inequalities (LMIs). Based on such conditions, we propose a robust H∞ sampled-data control design for an uncertain fuzzy system with discrete and distributed delays. Finally, we extend the result to a robust H∞ sampled-data control design for uncertain fuzzy systems with discrete and distributed delays.