A delay-range-partition approach to analyse stability of linear systems with time-varying delays

In this paper, the stability analysis of linear systems with an interval time-varying delay is investigated. First, augmented Lyapunov–Krasovskii functionals are constructed, which include more information of the delay's range and the delay's derivative. Second, two improved integral inequalities, which are less conservative than Jensen's integral inequalities, and delay-range-partition approach are utilised to estimate the upper bounds of the derivatives of the augmented Lyapunov–Krasovskii functionals. Then, less conservative stability criteria are proposed no matter whether the lower bound of delay is zero or not. Finally, to illustrate the effectiveness of the stability criteria proposed in this paper, two numerical examples are given and their results are compared with the existing results.