Stability of perturbed functional differential equations and stabilization of nonlinear cascades

In this paper the effect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability in preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. This results in a general framework, in which the stabilization of partial linear cascade systems using partial state feedback can be treated systematically.