Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay

Irada A. Dzhalladova; Jaromír Baštinec; Josef Diblík; Denys Y. Khusainov

doi:10.1155/2011/920412

Abstract and Applied Analysis (Jan 2011)

Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay

Irada A. Dzhalladova,
Jaromír Baštinec,
Josef Diblík,
Denys Y. Khusainov

Affiliations

Irada A. Dzhalladova: Department of Mathematics, Kyiv National Economic University, Peremogy Avenue, Kyiv 03038, Ukraine
Jaromír Baštinec: Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic
Josef Diblík: Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic
Denys Y. Khusainov: Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, Vladimirskaya Street, Kyiv 01601, Ukraine

DOI: https://doi.org/10.1155/2011/920412
Journal volume & issue: Vol. 2011

Abstract

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A nonlinear stochastic differential-difference control system with delay of neutral type is considered. Sufficient conditions for the exponential stability are derived by using Lyapunov-Krasovskii functionals of quadratic form with exponential factors. Upper bound estimates for the exponential rate of decay are derived.

Published in Abstract and Applied Analysis

ISSN: 1085-3375 (Print); 1687-0409 (Online)
Publisher: Wiley
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://onlinelibrary.wiley.com/journal/4058

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