Less conservative stability criteria for linear systems with interval time-varying delays

The problem of the stability of a linear system with an interval time-varying delay is investigated. A new Lyapunov-Krasovskii functional that fully uses information about the lower bound of the time-varying delay is constructed to derive new stability criteria. It is proved that the proposed Lyapunov-Krasovskii functional can lead to less conservative results than some existing ones. Based on the proposed Lyapunov-Krasovskii functional, two stability conditions are developed using two different methods to estimate Lyapunov-Krasovskii functional's derivative. Two numerical examples are given to illustrate that the two stability conditions are complementary and yield a larger maximum upper bound of the time-varying delay than some existing results.