Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls

Jiang, Yanan and Hu, Liangjian and Mao, Wei and Lu, Jianqiu and Mao, Xuerong (2023) Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls. Nonlinear Analysis: Hybrid Systems, 49. 101374. ISSN 1751-570X (https://doi.org/10.1016/j.nahs.2023.101374)

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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.

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