Lyapunov's direct method for stability of a set and its transitivity under a differential inclusion

Dai Zusai

No 3, TUPD Discussion Papers from Graduate School of Economics and Management, Tohoku University

Abstract: We present a version of Lyapunov's direct method for stability of a set under a differential inclusion. We pay careful attention to the assumption of forward invariance of a basin of attraction, which is often overlooked when applying the method to local stability. Even if the value of a local Lyapunoov function monotonically changes in some neighborhood of the limit set, this alone does not prevent a trajectory from escaping from this particular neighborhood. In this note, we verify that we can construct a smaller but forward invariant neighborhood. As a corollary, we obtain a transitivity theorem on basins of attractions without requiring forward invariance.

Pages: 14 pages
Date: 2021-05
New Economics Papers: this item is included in nep-gth
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10097/00131574

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:toh:tupdaa:3

Access Statistics for this paper

More papers in TUPD Discussion Papers from Graduate School of Economics and Management, Tohoku University Contact information at EDIRC.
Bibliographic data for series maintained by Tohoku University Library ().