On Necessity of Asymptotic Stability for Singularly Perturbed Systems

Abstract

The Klimushchev-Krasovskii condition is a sufficient condition for singularly perturbed systems to be asymptotically stable for sufficiently small parameters. This paper concerns whether the condition is also necessary. Descriptions on this issue in some literature are corrected. The corrected result is then proven through the notion of inertia of matrices.