Hierarchy of stability criterion for time-delay systems based on multiple integral approach

Taking a class of time-delay systems as research object, this brief aims at developing a theoretical support on the hierarchy of stability criterion which is derived by the multiple integral approach and free-weighting matrix technique. The hierarchy implies that the conservatism of stability criterion can be reduced by increasing the ply of integral terms in Lyapunov-Krasovskii functional (LKF). Together with three numerical experiments, the hierarchy of stability criterion is further shown.