Abstract and Applied Analysis
Volume 2011 (2011), Article ID 920412, 14 pages
http://dx.doi.org/10.1155/2011/920412
Research Article

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

Irada A. Dzhalladova,1 Jaromír Baštinec,2 Josef Diblík,2,3 and Denys Y. Khusainov4

1Department of Mathematics, Kyiv National Economic University, Peremogy Avenue, Kyiv 03038, Ukraine
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic
3Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 602 00 Brno, Czech Republic
4Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, Vladimirskaya Street, Kyiv 01601, Ukraine

Received 2 February 2011; Accepted 28 March 2011

Academic Editor: Miroslava Růžičková

Copyright © 2011 Irada A. Dzhalladova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.