The problem of exponential stability and stabilization is studied for a class of uncertain linear systems with time-varying delay. The time delay is a continuous function belonging to a given interval, which means that the lower and the upper bounds for the time-varying delay are available.
The distinctive features of the presented results are, by the author’s opinion, the following: the delay function is not necessary to be differentiable and the lower bound of the delay is not restricted to be zero. Notice that, in the most delay-dependent stability results for systems with time-varying delay, the time delay function is required to be differentiable and, moreover, the upper bound of the derivative is restricted to a number less than unity.
Based on the construction of some Lyapunov-Krasovskii functionals, new delay-dependent sufficient conditions for the exponential stabilization of the systems are established in terms of LMIs. Numerical examples are given to demonstrate the effectiveness of the derived conditions.