Stability of uncertain systems with time-varying delays

This paper provides a new criterion for robust asymptotical stability of a class of uncertain systems with multiple time-varying delays and nonlinear uncertainties based on LaSalle theorem. Firstly, we gave a contractive invariant set for time-delay systems, and then we derived the condition in which the system would be attracted into this invariant set based on LaSalle Theorem. Time delays are assumed to be arbitrary time-varying and upper-bounded. Compared with some existing results, our results are less conservative and easy to check. Numerical examples illustrate our main results