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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Veröffentlicht in:Computers & mathematics with applications (1987) Jg. 66; H. 11; S. 2295 - 2306
Hauptverfasser: Kadiev, Ramazan, Ponosov, Arcady
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.12.2013
Schlagworte:
Input-to-state stability
Lyapunov stability
Stochastic difference equations
Lyapunov stability
Stochastic difference equations
Input-to-state stability
ISSN:0898-1221, 1873-7668
Online-Zugang:Volltext
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Zusammenfassung: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