On the Klimushchev-Krasovskii theorem

The Klimushchev-Krasovskii theorem describes a sufficient condition for the asymptotic stability of singularly perturbed systems. Motivated by some subtle examples, this note presents a new necessary and sufficient condition by imposing an additional assumption on the statement of the Klimushchev-Krasovskii theorem. This note also extends the main inertia theorem to singularly perturbed systems.

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