Robust stability: perturbed systems with perturbed equilibria

Studies robustness properties of a large class of nonlinear systems by addressing the following question: given a nonlinear system with specified asymptotically stable equilibria, under what conditions will a perturbed model of the system possess asymptotically stable equilibria which are close (in distance) to the asymptotically stable equilibria of the unperturbed system? In arriving at their results, the authors establish robustness stability results for the perturbed systems considered herein and determine conditions which ensure the existence of asymptotically stable equilibria of the perturbed system which are near the asymptotically stable equilibria of the original unperturbed system. These results involve quantitative estimates of the distance between the corresponding equilibrium points of the unperturbed and perturbed systems. The authors apply the above results in the analysis of a large class of systems which arise in VLSI implementations of nonlinear (transistor) circuits