Stabilization of highly nonlinear hybrid systems driven by Lévy noise and delay feedback control based on discrete-time state observations

Seyfeddine Moualkia, Yong Xu

科研成果: 期刊稿件文章同行评审

13 引用 (Scopus)

摘要

There are many hybrid stochastic differential equations (SDEs) in the real-world that don't satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.

源语言英语
页(从-至)1005-1035
页数31
期刊Journal of the Franklin Institute
360
2
DOI
出版状态已出版 - 1月 2023

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