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Existence and Uniqueness and Stability of Solutions for Stochastic Impulsive Systems

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Abstract

This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stability of solutions for stochastic impulsive systems are established. Furthermore, the results are specialized to the case of linear stochastic impulsive systems. Finally, some examples are given to illustrate the applications of our theory.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Bin Liu, Xinzhi Liu & Xiaoxin Liao

  2. Department of Information and Computation Science, Zhuzhou Institute of Technology, Zhuzhou, 412008, China

    Bin Liu

  3. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Xinzhi Liu

Authors
  1. Bin Liu
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  2. Xinzhi Liu
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  3. Xiaoxin Liao
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Corresponding author

Correspondence to Bin Liu.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 60274007, and the Post Doctoral Foundation of China and the Excellent Young Program of the Education Department of Hunan Province under Grant No. 04B068, and the NSERC-Canada.

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Liu, B., Liu, X. & Liao, X. Existence and Uniqueness and Stability of Solutions for Stochastic Impulsive Systems. Jrl Syst Sci & Complex 20, 149–158 (2007). https://doi.org/10.1007/s11424-007-9013-6

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  • DOI: https://doi.org/10.1007/s11424-007-9013-6

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