Stabilization by intermittent control for hybrid stochastic differential delay equations

Wei Mao; Yanan Jiang; Liangjian Hu; Xuerong Mao

doi:10.3934/dcdsb.2021055

Article Contents

2022, Volume 27, Issue 1: 569-581. Doi: 10.3934/dcdsb.2021055

This issue Previous Article A learning-enhanced projection method for solving convex feasibility problems Next Article Asymptotics of singularly perturbed damped wave equations with super-cubic exponent

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
^* Corresponding author: Liangjian Hu

Received: July 31, 2020

Revised: December 31, 2020

Early access: February 2021

Published: January 2022

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)

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Abstract

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.

Keywords:

Stochastic stabilization,
hybrid stochastic differential equations,
intermittent control,
delay observation.

Mathematics Subject Classification: Primary: 60H10, 93E15.

Citation:

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Figure 1. The sample paths of the hybrid differential equations (21)

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Figure 2. The sample paths of the intermittently hybrid SDEs (22) with $ \theta = 0.95 $

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Figure 3. The sample paths of the intermittently hybrid SDDEs (23)

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