Lyapunov-Krasovskij approach to the robust stability analysis of time-delay systems (Q1858365)

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.