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Chain prolongation and chain stability

✍ Scribed by Changming Ding

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 233 KB
Volume: 68
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2007.02.018

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✦ Synopsis

In this article we introduce chain prolongation, with which we define the concept of chain stability that takes an intermediate position between absolute stability and asymptotic stability. Two characterizations of chain stability are given, in terms of a Lyapunov function and a fundamental system of neighborhoods. As a matter of fact, a positively invariant compact set is chain stable if and only if it is a quasi-attracting set.

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