Robust H∞ control of linear systems with interval non-differentiable time-varying delays

In this paper, robust H_∞ control for a class of linear systems with time-varying delay is studied. The time delay is a continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, but the delay function is not necessarily differentiable. Based on Lyapunov-Krasovskii theory combined with Leibniz-Newton´s formula, new delay-dependent sufficient conditions for the exponential stabilization and a prescribed H_∞ performance level of the closed-loop system for all admissible uncertainties, are established in terms of LMIs. Numerical examples are given to illustrate the effectiveness of the theoretical results.