Guaranteed cost control of nonlinear systems with interval time-varying delays

In this paper, guaranteed cost control for a class of nonlinear 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 novel criteria for the existence of guaranteed cost controllers are established in terms of LMIs. Numerical examples are given to illustrate the effectiveness of the theoretical results.