Complex 2004 Proceedings of the 7th Asia-Pacific Conference on Complex Systems Cairns Convention Centre, Cairns, Australia 6-10th December 2004 Delay-dependent robust stability for uncertain linear systems with interval time-varying delay Xiefu Jiang and Qing-Long Han Faculty of Informatics and Communication, Central Queensland University, Rockhampton, QLD 4702, Australia Email: {x.jiang,q.han}@cqu.edu.au Abstract This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time- varying delay is needed, which allows the delay to be a fast time-varying function. The uncertainty under consideration is norm-bounded, and possibly time-varying, uncertainty. Based on a Lyapunov-Krasovskii functional approach, a stability cri- terion is derived by introducing some free weighting matrices that can be used to reduce the conservatism of the criterion. Numerical examples are given to demon- strate effectiveness of the proposed method. 1. Introduction The stability of time-delay systems has been widely investigated in the last two decades, see for example (Gu et al., 2003) and references therein. Practical examples of time-delay systems include chemical engineering, communications and biological systems (Hale and Lunel, 1993; Kuang, 1993). Current efforts can be divided into two classes: namely, frequency-domain approach and time-domain approach. In the time-domain approach, the direct Lyapunov method is a powerful tool. There are two different ideas how one can use this method. They are the Lyapunov-Krasovskii approach and the Lyapunov-Razumikhin approach. Both approaches can be used to han- dle systems with time-varying delay. The former usually requires both the upper bound of the time-varying delay and additional information on the derivative of the time-varying delay (Han, 2003; Han, 2004), while the latter has no restriction on the derivative of the time-varying delay, which allows a fast time-varying delay (Li and Souza, 1997). The ob- tained results using the Lyapunov-Krasovskii approach are usually less conservative than those using the Lyapunov-Razumikhin approach since the former takes advantage of the additional information of the delay. It is well known that there are systems which are stable with some nonzero delay, but are unstable without delay (Gu, 2001; Gu et al., 2001). For such case, if there is a