Singular perturbations, large-scale systems and asymptotic stability of invariant sets

Abstract

The paper deals with asymptotic stability of invariant sets of large-scale non-linear time-varying systems subjected to singular perturbations and possibly to external disturbances and arbitrary structural variations.

New aggregation of the systems proposed in the paper reduces the asymptotic stability test to verification of negative definiteness of lower order symmetric aggregation matrices that are independent of small parameters.