Research ArticleImproved delay-range-dependent robust stability for uncertain systems with interval time-varying delay

- This paper has presented improved delay-range-dependent robust stability for uncertain systems with interval time-varying delay.
- Lyapunov-Krasovskii functional and delayed decomposition approach are combined to investigate the problem.
- The proposed criteria are computationally attractive, and it provides less conservative results than the existing results.
- Four well-known examples show that these methods reduced conservatism and improved the maximal allowable delay.

This paper is concerned with the improved delay-range-dependent stability and robust stability criteria for linear systems with time-varying delay and norm-bounded uncertainties. In order to obtain much less conservative criteria, a Lyapunov-Krasovskii functional (LKF), which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to derive new stability criteria. By using delayed decomposition approach (DDA), a tighter upper bound of the derivative of Lyapunov functional can be obtained, and thus the proposed criteria give results with less conservatism compared with some previous ones. The resulting criteria have advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which are established theoretically. We show, by four well known examples, that our result overcomes the previous allowable maximum admissible upper bound (MAUB) of the time-delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay.