Discrete Filippov-Type Stability for One-Sided Lipschitzian Difference Inclusions

Robert Baier () and Elza Farkhi ()
Additional contact information
Robert Baier: University of Bayreuth
Elza Farkhi: Tel Aviv University

A chapter in Control Systems and Mathematical Methods in Economics, 2018, pp 27-55 from Springer

Abstract: Abstract We state and prove Filippov-type stability theorems for discrete difference inclusions obtained by the Euler discretization of a differential inclusion with perturbations in the set of initial points, in the right-hand side and in the state variable. We study the cases in which the right-hand side of the inclusion is not necessarily Lipschitz, but satisfies a weaker one-sided Lipschitz (OSL) or strengthened one-sided Lipschitz (SOSL) condition. The obtained estimates imply stability of the discrete solutions for infinite number of fixed time steps if the OSL constant is negative and the perturbations are bounded in certain norms. We show a better order of stability for SOSL right-hand sides and apply our theorems to estimate the distance from the solutions of other difference methods, as for the implicit Euler scheme to the set of solutions of the Euler scheme. We also prove a discrete relaxation stability theorem for the considered difference inclusion, which also extends a theorem of Grammel (Set-Valued Anal. 11(1):1–8, 2003) from the class of Lipschitz maps to the wider class of OSL ones.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:lnechp:978-3-319-75169-6_3

Ordering information: This item can be ordered from
http://www.springer.com/9783319751696

DOI: 10.1007/978-3-319-75169-6_3

Access Statistics for this chapter

More chapters in Lecture Notes in Economics and Mathematical Systems from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().