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Effects of commensurable delays in the stability of difference equations

Published online by Cambridge University Press:  14 November 2011

José M. Ferreira
José M. Ferreira
Affiliation:
Centro de Física da Matéria Condensada, (I.N.I.C.), Av. Prof. Gama Pinto, 2, 1699 Lisboa-Codex, Portugal
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Synopsis

This paper studies how, in a difference equation, uniform asymptotic stability for commensurable delays implies uniform asymptotic stability globally in the delays. A result is also given on renorming the space C= C([ – ∥r∥, 0]; ℂn so that a difference operator has norm less than one if it is uniformly asymptotically stable globally in the delays.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 3-4 , 1985 , pp. 191 - 199
Copyright
Copyright © Royal Society of Edinburgh 1985

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