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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Vydané v:Computers & mathematics with applications (1987) Ročník 66; číslo 11; s. 2295 - 2306
Hlavní autori: Kadiev, Ramazan, Ponosov, Arcady
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Ltd 01.12.2013
Predmet:
Input-to-state stability
Lyapunov stability
Stochastic difference equations
Lyapunov stability
Stochastic difference equations
Input-to-state stability
ISSN:0898-1221, 1873-7668
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Abstract 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.
AbstractList 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.
Author Kadiev, Ramazan
Ponosov, Arcady
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Cites_doi 10.1016/j.jmaa.2004.09.042
10.1016/j.jmaa.2012.01.003
10.1080/10236198.2010.531276
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Issue 11
Keywords Lyapunov stability
Stochastic difference equations
Input-to-state stability
Language English
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SubjectTerms Input-to-state stability
Lyapunov stability
Stochastic difference equations
Title Exponential stability of Itô-type linear functional difference equations
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