Lyapunov Stability of Differential Inclusions Involving Prox-Regular Sets via Maximal Monotone Operators

Samir Adly (), Abderrahim Hantoute () and Bao Tran Nguyen ()
Additional contact information
Samir Adly: Université de Limoges
Abderrahim Hantoute: Universidad de Chile
Bao Tran Nguyen: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 3, 906-934

Abstract: Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed remodeled into the classical theory of differential inclusions, involving maximal monotone operators. This result is new in the literature. It permits to make use of the rich and abundant achievements in the class of monotone operators to study different stability aspects, and to give new proofs for the existence, the continuity, and the differentiability of solutions. This going back and forth between these two models of differential inclusions is made possible thanks to a viability result for maximal monotone operators. Applications will concern Luenberger-like observers associated with these differential inclusions.

Keywords: Differential inclusions; Prox-regular sets; Maximal monotone operators; Lyapunov functions; a-Lyapunov pairs; Invariant sets; Observer designs; 34A60; 34D05; 37B25; 49J15; 47H05; 49J52; 93B05 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1446-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-018-1446-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-1446-7

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().