Stability in delay equations with perturbed time lags

Studies the effects of perturbations of time delays on the stability of a class of delay equations. The authors´ goal is to obtain a “practical” condition, i.e., a norm bound on the perturbations corresponding to the particular system under consideration, which guarantees the preservation of stability under perturbations. It turns out that such condition can be formulated assuming that one knows the fundamental solution of the unperturbed system. Since stability of the unperturbed system implies that the components of its fundamental solution go to zero at infinity, it is possible to get “good” numerical estimates of these components, and consequently obtain norm bounds on the allowable perturbations. The authors present their main results and consider numerical examples. The authors demonstrate how their results can be used to obtain an estimation of the maximum allowable sampling interval in the stability of a hybrid system with feedback delay