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Lyapunov-Krasovskij approach to the robust stability analysis of time-delay systems. (English) Zbl 1014.93031

The Andronov-Witt theorem on “constantly acting perturbations” of ordinary differential equations (ODEs) is extended to linear ODEs with constant delays. The well-known necessary condition of ‘strong’ asymptotic (Lyapunov-) stability in the absence of perturbations is established by means of a quadratic Krasovskij \(V\)-functional, followed by an estimate of the perturbations on its \(V'\)-boundedness.
Since terms of dependent variables are allowed in the perturbations, only local robustness can be claimed without further analysis, because a small factor does not always imply that the product of dependent variables is negligible globally.

MSC:

93D09 Robust stability
93C73 Perturbations in control/observation systems
34K20 Stability theory of functional-differential equations
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References:

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