Exponential stability of Itô-type linear functional difference equations

We study the stability properties of rather general linear stochastic functional difference equations and offer a partial justification of an important result in the stability analysis, which is known as “the Bohl–Perron principle” and which helps us to deduce exponential Lyapunov stability from the...

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Bibliographic Details
Published in:	Computers & mathematics with applications (1987) Vol. 66; no. 11; pp. 2295 - 2306
Main Authors:	Kadiev, Ramazan, Ponosov, Arcady
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.12.2013
Subjects:	Input-to-state stability Lyapunov stability Stochastic difference equations Lyapunov stability Stochastic difference equations Input-to-state stability
ISSN:	0898-1221, 1873-7668
Online Access:	Get full text
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Summary:	We study the stability properties of rather general linear stochastic functional difference equations and offer a partial justification of an important result in the stability analysis, which is known as “the Bohl–Perron principle” and which helps us to deduce exponential Lyapunov stability from the input-to-state stability with respect to non-weighted functional spaces. We use a special technique based on integral regularization, which proved to be powerful in the general theory of linear functional differential and difference equations. In addition to the general framework, we provide a number of examples demonstrating the efficiency of our results.
ISSN:	0898-1221 1873-7668
DOI:	10.1016/j.camwa.2013.06.012