Improved robust stability criteria for time-delay systems

The delay-dependent robust stability for uncertain time-delay systems is investigated in this paper. Firstly, a novel augmented Lyapunov-Krasovskii functional is constructed and its positive definiteness is proved. Then, some slack matrices are used in order to avoid using any bounding techniques, and as a result, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities, and it is also theoretically established that the obtained results are less conservative than some existing stability conditions. Finally, numerical examples are also given to illustrate the significant improvement on the conservatism of the delay bound over some existing results.