Stabilization for hybrid stochastic differential equations driven by Lévy noise via periodically intermittent control

Yong Ren; Qi Zhang

doi:10.3934/dcdsb.2021207

Article Contents

2022, Volume 27, Issue 7: 3811-3829. Doi: 10.3934/dcdsb.2021207

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Stabilization for hybrid stochastic differential equations driven by Lévy noise via periodically intermittent control

Yong Ren^, and
Qi Zhang

Department of Mathematics, Anhui Normal University, Wuhu 241000, China

^* Corresponding author: Yong Ren
^* Corresponding author: Yong Ren

Received: January 31, 2020

Revised: June 30, 2021

Published: July 2022

This work is supported by the NNSF of China (11871076)

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Abstract

In this work, the issue of stabilization for a class of continuous-time hybrid stochastic systems with Lévy noise (HLSDEs, in short) is explored by using periodic intermittent control. As for the unstable HLSDEs, we design a periodic intermittent controller. The main idea is to compare the controlled system with a stabilized one with a periodic intermittent drift coefficient, which enables us to use the existing stability results on the HLSDEs. An illustrative example is proposed to show the feasibility of the obtained result.

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Mathematics Subject Classification: Primary: 93D15; Secondary: 60H10, 60J75.

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Figure 1. The paths of the solution $ Y(s) $ to the system (39) for state 1

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Figure 2. The paths of the solution $ Y(s) $ to the system (40) for state 1

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Figure 3. The paths of the solution $ Y(s) $ to the system (39) for state 2

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Figure 4. The paths of the solution $ Y(s) $ to the system (40) for state 2

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