Stabilization of stochastic systems driven by $ G $-Lévy process via discrete-time feedback control

Guanghua Wei; Bingjun Wang; Mingxia Yuan; Guanghua Wei; Bingjun Wang; Mingxia Yuan

doi:10.3934/math.20251282

AIMS Mathematics

2025, Volume 10, Issue 12: 29151-29167. doi: 10.3934/math.20251282

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Research article

Stabilization of stochastic systems driven by $ G $-Lévy process via discrete-time feedback control

1.
Jinling Institute of Technology, Nanjing, 211169, China
2.
Jiangsu Key Lab for NSLSCS, Nanjing Normal University, Nanjing, 210023, China
3.
Nanjing Vocational Institute of Transport Technology, Nanjing, 211188, China

Received: 09 September 2025 Revised: 16 November 2025 Accepted: 03 December 2025 Published: 11 December 2025
MSC : 60H05, 60H10, 60H20

In this paper, we establish sufficient conditions for the mean square and quasi-sure exponential stability of stochastic differential equations driven by the $ G $-Lévy process under discrete-time feedback control in the drift term. Departing from the conventional Lyapunov-based approach, we propose a comparative method to analyze the stabilization effect of the designed control. An example validates the effectiveness of the proposed control strategy.
- $ G $-Lévy process,
- discrete-time feedback,
- stability
Citation: Guanghua Wei, Bingjun Wang, Mingxia Yuan. Stabilization of stochastic systems driven by $ G $-Lévy process via discrete-time feedback control[J]. AIMS Mathematics, 2025, 10(12): 29151-29167. doi: 10.3934/math.20251282

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Abstract

In this paper, we establish sufficient conditions for the mean square and quasi-sure exponential stability of stochastic differential equations driven by the $ G $-Lévy process under discrete-time feedback control in the drift term. Departing from the conventional Lyapunov-based approach, we propose a comparative method to analyze the stabilization effect of the designed control. An example validates the effectiveness of the proposed control strategy.

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