# American Institute of Mathematical Sciences

January  2022, 27(1): 569-581. doi: 10.3934/dcdsb.2021055

## Stabilization by intermittent control for hybrid stochastic differential delay equations

 1 School of mathematics and information technology, Jiangsu Second Normal University, Nanjing, 210013, China 2 College of Information Sciences and Technology, Donghua University, Shanghai, 201620, China 3 Department of Applied Mathematics, Donghua University, Shanghai 201620, China 4 Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, U.K

* Corresponding author: Liangjian Hu

Received  August 2020 Revised  January 2021 Published  January 2022 Early access  February 2021

Fund Project: The research of W.Mao was supported by the National Natural Science Foundation of China(11401261), "333 High-level Project" of Jiangsu Province and the Qing Lan Project of Jiangsu Province. The research of L.Hu was supported by the National Natural Science Foundation of China (11471071). The research of X.Mao was supported by the Leverhulme Trust (RF-2015-385), the Royal Society (WM160014, Royal Society Wolfson Research Merit Award), the Royal Society and the Newton Fund (NA160317, Royal Society-Newton Advanced Fellowship), the EPSRC (EP/K503174/1)

This paper is concerned with stablization of hybrid differential equations by intermittent control based on delay observations. By M-matrix theory and intermittent control strategy, we establish a sufficient stability criterion on intermittent hybrid stochastic differential equations. Meantime, we show that hybrid differential equations can be stabilized by intermittent control based on delay observations if the delay time $\tau$ is bounded by $\tau^*$. Finally, an example is presented to illustrate our theory.

Citation: Wei Mao, Yanan Jiang, Liangjian Hu, Xuerong Mao. Stabilization by intermittent control for hybrid stochastic differential delay equations. Discrete & Continuous Dynamical Systems - B, 2022, 27 (1) : 569-581. doi: 10.3934/dcdsb.2021055
##### References:

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##### References:
The sample paths of the hybrid differential equations (21)
The sample paths of the intermittently hybrid SDEs (22) with $\theta = 0.95$
The sample paths of the intermittently hybrid SDDEs (23)
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