Exponential Stability of Stochastic Systems with Delay and Poisson Jumps
Joint Authors
Zhu, Wenli
Zhao, Zhao
Huang, Jiexiang
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-05
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
This paper focuses on the model of a class of nonlinear stochastic delay systems with Poisson jumps based on Lyapunov stability theory, stochastic analysis, and inequality technique.
The existence and uniqueness of the adapted solution to such systems are proved by applying the fixed point theorem.
By constructing a Lyapunov function and using Doob’s martingale inequality and Borel-Cantelli lemma, sufficient conditions are given to establish the exponential stability in the mean square of such systems, and we prove that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable.
The obtained results show that if stochastic systems is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic delay systems with Poisson jumps will remain exponentially stable, and time delay upper limit is solved by using the obtained results when the system is exponentially stable, and they are more easily verified and applied in practice.
American Psychological Association (APA)
Zhu, Wenli& Huang, Jiexiang& Zhao, Zhao. 2014. Exponential Stability of Stochastic Systems with Delay and Poisson Jumps. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-506765
Modern Language Association (MLA)
Zhu, Wenli…[et al.]. Exponential Stability of Stochastic Systems with Delay and Poisson Jumps. Mathematical Problems in Engineering No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-506765
American Medical Association (AMA)
Zhu, Wenli& Huang, Jiexiang& Zhao, Zhao. Exponential Stability of Stochastic Systems with Delay and Poisson Jumps. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-506765
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-506765