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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 707069, 8 pages
http://dx.doi.org/10.1155/2015/707069
Research Article

Boundedness of Stochastic Delay Differential Systems with Impulsive Control and Impulsive Disturbance

1Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
2Control and Simulation Center, Harbin Institute of Technology, Harbin 150001, China

Received 27 February 2014; Accepted 5 August 2014

Academic Editor: Weihai Zhang

Copyright © 2015 Liming Wang 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

This paper considers the -moment boundedness of nonlinear impulsive stochastic delay differential systems (ISDDSs). Using the Lyapunov-Razumikhin method and stochastic analysis techniques, we obtain sufficient conditions which guarantee the -moment boundedness of ISDDSs. Two cases are considered, one is that the stochastic delay differential system (SDDS) may not be bounded, and how an impulsive strategy should be taken to make the SDDS be bounded. The other is that the SDDS is bounded, and an impulsive disturbance appears in this SDDS, then what restrictions on the impulsive disturbance should be adopted to maintain the boundedness of the SDDS. Our results provide sufficient criteria for these two cases. At last, two examples are given to illustrate the correctness of our results.