This paper is concerned with robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay\r\nis assumed to belong to an interval, which means that the derivative of the time-varying delay has an upper bound or a restriction.\r\nOn other occasions, if we do not take restriction on the derivative of the time-varying delay into consideration, it allows the\r\ndelay to be a fast time-varying function. The uncertainty under consideration includes a polytopic-type uncertainty and a linear\r\nfractional norm-bounded uncertainty. In order to obtain much less conservative results, a new Lyapunov-Krasovskii functional,\r\nwhich makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to derive\r\nsome new stability criteria. Numerical examples are given to demonstrate the effectiveness of the proposed stability criteria
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