Razumikhin-type theorems on polynomial stability of hybrid stochastic systems with pantograph delay

Wei Mao; Liangjian Hu; Xuerong Mao

doi:10.3934/dcdsb.2020059

Article Contents

2020, Volume 25, Issue 8: 3217-3232. Doi: 10.3934/dcdsb.2020059

This issue Previous Article Exit problem for Ornstein-Uhlenbeck processes: A random walk approach Next Article Random attractor for stochastic Hindmarsh-Rose equations with multiplicative noise

Razumikhin-type theorems on polynomial stability of hybrid stochastic systems with pantograph delay

1.
School of mathematics and information technology, Jiangsu Second Normal University, Nanjing 210013, China
2.
Department of Applied Mathematics, Donghua University, Shanghai 201620, China
3.
Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK

^* Corresponding author: Liangjian Hu
^* Corresponding author: Liangjian Hu

Received: July 2019

Revised: September 2019

Early access: February 2020

Published: August 2020

The author Wei Mao is supported by the National Natural Science Foundation of China (11401261) and "333 High-level Personnel Training Project" of Jiangsu Province. The author Liangjian Hu is supported by the National Natural Science Foundation of China (11471071). The author Xuerong Mao is 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

The main aim of this paper is to investigate the polynomial stability of hybrid stochastic systems with pantograph delay (HSSwPD). By using the Razumikhin technique and Lyapunov functions, we establish several Razumikhin-type theorems on the $ p $th moment polynomial stability and almost sure polynomial stability for HSSwPD. For linear HSSwPD, sufficient conditions for polynomial stability are presented.

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

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