Absolute stability in linear delay-differential systems: ill-posedness and robustness

The author considers matrix delay-differential systems which are polynomial in several delay operators. Using a necessary and sufficient criterion for stability independent of delay, or absolute stability, the author shows that system stability for all values of the delay vector lying in a sector will imply absolute stability. We then show that absolute stability is ill-posed with respect to arbitrarily small perturbations of the delay ratios if a certain extended delay-differential system which is formed from the original is not also absolutely stable.