A less conservative robust stability test for linear uncertain time-delay systems

This note concerns with the robust stability of linear uncertain systems with state-delay. The uncertainty is assumed to be of polytopic type. A less conservative delay-dependent linear matrix inequality (LMI) method is presented based on a new Lyapunov-Krasovskii functional. The present method incorporates a relaxed parameter-dependent technique combined with a recently proposed idea of introducing free-weighting matrices. When confined to delay-free case, the present result is also less conservative than existing stability tests using parameter-dependent methods. Numerical examples are given to show the less conservativeness of the results.