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Discrete-time feedback stabilization for neutral stochastic functional differential equations driven by G-Lévy process

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  • Yuan, Haiyan
  • Zhu, Quanxin

Abstract

This paper mainly discusses the exponential stability of neutral stochastic functional differential equations with G-Lévy jump. For a given mean square exponential unstable neutral stochastic differential equations with G-Lévy jump, a discrete-time feedback control in the drift part is designed to realize feedback stability and the H∞ stable càdlàg solution of corresponding systems is obtained. The upper bound of state observation duration of the corresponding systems is derived by extending Mao′s method. Further up, the exponential stabilization conditions are established and some exponential stabilities of the solutions are proved by using the G-Lyapunov functional method. Moreover, an example is presented to verify the obtained results.

Suggested Citation

  • Yuan, Haiyan & Zhu, Quanxin, 2023. "Discrete-time feedback stabilization for neutral stochastic functional differential equations driven by G-Lévy process," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011602
    DOI: 10.1016/j.chaos.2022.112981
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    References listed on IDEAS

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    1. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    2. Ren, Liying, 2013. "On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1301-1310.
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    Cited by:

    1. Yuan, Haiyan & Zhu, Quanxin, 2024. "Practical stability of the analytical and numerical solutions of stochastic delay differential equations driven by G-Brownian motion via some novel techniques," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. Yang, Xuetao & Zhu, Quanxin, 2024. "Stabilization of stochastic nonlinear systems via double-event-triggering mechanisms and switching controls," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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