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Exponential stability and interval stability of a class of stochastic hybrid systems driven by both Brownian motion and Poisson jumps

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  • Sun, Mingmei
  • Xu, Meng

Abstract

A class of stochastic singular hybrid systems driven by both Brownian motion and Poisson jumps are studied. This paper is devoted to discussing the exponential stability and interval stability of such stochastic singular hybrid systems. The concept of interval admissibility is proposed. Sufficient conditions are given for exponential mean square admissibility and interval admissibility by using Itô’s formula, H-representation and spectrum technique. Finally, two simulation cases are presented to demonstrate the theoretical results.

Suggested Citation

  • Sun, Mingmei & Xu, Meng, 2017. "Exponential stability and interval stability of a class of stochastic hybrid systems driven by both Brownian motion and Poisson jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 58-73.
    • Handle: RePEc:eee:phsmap:v:487:y:2017:i:c:p:58-73
    DOI: 10.1016/j.physa.2017.05.071
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    References listed on IDEAS

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    1. Chavanis, Pierre-Henri, 2008. "Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5716-5740.
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    3. Wang, Ying & Huang, Zhen, 2009. "Backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1438-1443, June.
    4. Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2012. "Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5839-5849.
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    Cited by:

    1. Wang, Jufeng & Zhou, MengChu & Liu, Chunfeng, 2018. "Stochastic stability of Markovian jump linear systems over networks with random quantization density and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1128-1139.
    2. Yan, Zhiguo & Zhang, Min & Chang, Gaizhen & Lv, Hui & Park, Ju H., 2022. "Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach," Applied Mathematics and Computation, Elsevier, vol. 412(C).

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