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LMI approach to exponential stability of linear systems with interval time-varying delays. (English) Zbl 1230.93076

Summary: This paper addresses exponential stability problem for a class of linear systems with time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with the Newton-Leibniz formula technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of Linear Matrix Inequalities (LMIs). An application to exponential stability of uncertain linear systems with interval time-varying delay is given. Numerical examples are given to show the effectiveness of the obtained results.

MSC:

93D20 Asymptotic stability in control theory
93C05 Linear systems in control theory
15A09 Theory of matrix inversion and generalized inverses
52A10 Convex sets in \(2\) dimensions (including convex curves)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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