Stability of Time-delay System with Time-varying Uncertainties via Homogeneous Polynomial Lyapunov-Krasovskii Functions

This paper deals with the robust stability of time-delay system with time-varying uncertainties via homogeneous polynomial Lyapunov-Krasovskii functions (HPLKF). We give a sufficient condition to demonstrate that the system is asymptotically stable. A new class of Lyapunov-Krasovskii function is introduced, whose main feature is that the conservativeness due to uncertainties is reduced. Numerical examples illustrate the effectiveness of our method.