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Stability of Stochastic Impulsive Systems with Time Delay

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Abstract

In this chapter, we consider nonlinear stochastic impulsive systems with time delay. Particularly, the time delay here is finite; the stochastic noise is represented by a Wiener process, and the impulses are state-independent and are of types diminishing and unbounded in total.

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References

  1. Liu XZ, Ballinger GH (2001) Uniform asymptotic stability of impulsive delay differential equations. Comput Math Appl 41:903–915

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  2. Lakshmiknatham V, Bainov DD, Simeonov PS (1989) Theory of impulsive differential equations. World Scientific, Singapore

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  3. Alwan MS, Liu XZ, Xie W-C. (2013) Stability properties of nonlinear stochastic impulsive systems with time delay. J Nonlinear Syst Appl:86–91

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  4. Ballinger GH (1999) Qualitative theory of impulsive delay differential equations. PhD thesis, University of Waterloo, On, Canada

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Correspondence to Mohamad S. Alwan .

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© 2018 Springer Nature Singapore Pte Ltd. and Higher Education Press, Beijing

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Alwan, M.S., Liu, X. (2018). Stability of Stochastic Impulsive Systems with Time Delay. In: Theory of Hybrid Systems: Deterministic and Stochastic. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-10-8046-3_4

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