K. Wang et An. Michel, ROBUSTNESS AND PERTURBATION ANALYSIS OF A CLASS OF NONLINEAR-SYSTEMS WITH APPLICATIONS TO NEURAL NETWORKS, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 41(1), 1994, pp. 24-32
In this paper we study the robustness properties of a large class of n
onlinear systems by addressing the following question: given a nonline
ar system with specified asymptotically stable equilibria, under what
conditions will a perturbed model of the system possess asymptotically
stable equilibria that are close (in distance) to the asymptotically
stable equilibria of the unperturbed system? In arriving at our result
s, we establish robustness stability results for the perturbed systems
considered, and we determine conditions that ensure the existence of
asymptotically stable equilibria of the perturbed system that are near
the asymptotically stable equilibria of the original unperturbed syst
em. These results involve quantitative estimates of the distance betwe
en the corresponding equilibrium points of the unperturbed and perturb
ed systems. We apply the above results in the qualitative analysis of
a large class of artificial neural networks.