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Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays. (English) Zbl 1241.34080
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.

34K20Stability theory of functional-differential equations
34K06Linear functional-differential equations
34K27Perturbations of functional-differential equations
34K35Functional-differential equations connected with control problems
Full Text: DOI
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