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Almost sure exponential stability and stabilization of hybrid stochastic functional differential equations with Lévy noise

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Abstract

This paper uses the stationary distribution of Markov chains to obtain new criteria for the almost sure exponential stability of nonlinear hybrid stochastic functional differential equations with Lévy noise (HSFDEs-LN) under weaker conditions and an upper bound \(\tau ^{*}\) of time delay is obtained. That is, if corresponding HSDEs-LN is almost surely exponentially stable, then the HSFDEs-LN is also almost surely exponentially stable as long as time delay \(\tau <\tau ^{*}\). Furthermore, the new theory enabled us to design discrete-time state observations feedback control by using Lévy noise as the control source to stabilize a class of unstable hybrid differential equations.

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Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their constructive comments and suggestions which improved the quality of the paper. This research was supported by the National Natural Science Foundation of China (11771001), the Key Natural Science Research Project of Universities of Anhui Province, China (2022AH050108,22020721025).

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Xin Liu & Pei Cheng

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  1. Xin Liu
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  2. Pei Cheng
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Correspondence to Pei Cheng.

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Liu, X., Cheng, P. Almost sure exponential stability and stabilization of hybrid stochastic functional differential equations with Lévy noise. J. Appl. Math. Comput. 69, 3433–3458 (2023). https://doi.org/10.1007/s12190-023-01882-8

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