Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls

Yanan Jiang; Liangjian Hu; Wei Mao; Jianqiu Lu; Xuerong Mao

doi:10.1016/j.nahs.2023.101374

Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls

Yanan Jiang, Liangjian Hu, Wei Mao, Jianqiu Lu, Xuerong Mao

Mathematics And Statistics

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Abstract

In this paper, stabilization in distribution of hybrid stochastic differential equations (HSDEs) via periodically intermittent feedback controls is investigated. It is revealed that probability distributions of the solution will converge to a stationary distribution is revealed. Firstly, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for stabilization in distribution of HSDEs. Then, we prove the existence and uniqueness of invariant probability distribution, the lower bound of the intermittent parameter δ ^∗ is obtained. Three numerical examples are discussed to support our results of theoretical analysis.

Original language	English
Article number	101374
Journal	Nonlinear Analysis: Hybrid Systems
Volume	49
Early online date	19 May 2023
DOIs	https://doi.org/10.1016/j.nahs.2023.101374
Publication status	Published - 1 Aug 2023

Keywords

hybrid stochastic differential equations (HSDEs)

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10.1016/j.nahs.2023.101374

Jiang-etal-NAHS-2023-Stablisation-in-distribution-of-hybrid-stochastic-systemsAccepted author manuscript, 1.14 MBLicence: CC BY-NC-ND 4.0

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title = "Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls",

abstract = "In this paper, stabilization in distribution of hybrid stochastic differential equations (HSDEs) via periodically intermittent feedback controls is investigated. It is revealed that probability distributions of the solution will converge to a stationary distribution is revealed. Firstly, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for stabilization in distribution of HSDEs. Then, we prove the existence and uniqueness of invariant probability distribution, the lower bound of the intermittent parameter δ ∗ is obtained. Three numerical examples are discussed to support our results of theoretical analysis.",

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T1 - Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls

AU - Jiang, Yanan

AU - Hu, Liangjian

AU - Mao, Wei

AU - Lu, Jianqiu

AU - Mao, Xuerong

PY - 2023/8/1

Y1 - 2023/8/1

N2 - In this paper, stabilization in distribution of hybrid stochastic differential equations (HSDEs) via periodically intermittent feedback controls is investigated. It is revealed that probability distributions of the solution will converge to a stationary distribution is revealed. Firstly, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for stabilization in distribution of HSDEs. Then, we prove the existence and uniqueness of invariant probability distribution, the lower bound of the intermittent parameter δ ∗ is obtained. Three numerical examples are discussed to support our results of theoretical analysis.

AB - In this paper, stabilization in distribution of hybrid stochastic differential equations (HSDEs) via periodically intermittent feedback controls is investigated. It is revealed that probability distributions of the solution will converge to a stationary distribution is revealed. Firstly, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for stabilization in distribution of HSDEs. Then, we prove the existence and uniqueness of invariant probability distribution, the lower bound of the intermittent parameter δ ∗ is obtained. Three numerical examples are discussed to support our results of theoretical analysis.

KW - hybrid stochastic differential equations (HSDEs)

UR - https://www.sciencedirect.com/journal/nonlinear-analysis-hybrid-systems

U2 - 10.1016/j.nahs.2023.101374

DO - 10.1016/j.nahs.2023.101374

M3 - Article

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VL - 49

JO - Nonlinear Analysis: Hybrid Systems

JF - Nonlinear Analysis: Hybrid Systems

M1 - 101374

ER -

Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls

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Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Long-time dynamics of numerical solutions of stochastic differential equations

Cite this

Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Long-time dynamics of numerical solutions of stochastic differential equations

Cite this