Quasi sure exponential stabilization of nonlinear systems via intermittent $ G $-Brownian motion

Yong Ren; Wensheng Yin

doi:10.3934/dcdsb.2019110

Article Contents

2019, Volume 24, Issue 11: 5871-5883. Doi: 10.3934/dcdsb.2019110

This issue Previous Article Modelling the effects of contaminated environments in mainland China on seasonal HFMD infections and the potential benefit of a pulse vaccination strategy Next Article On the limit cycles of planar discontinuous piecewise linear differential systems with a unique equilibrium

Quasi sure exponential stabilization of nonlinear systems via intermittent $ G $-Brownian motion

Yong Ren^1, , and
Wensheng Yin^2,

1.
Department of Mathematics, Anhui Normal University, Wuhu 241000, China
2.
School of Mathematics, Southeast University, Nanjing 211189, China

^* Corresponding author
^* Corresponding author

Received: September 2018

Early access: June 2019

Published: August 2019

This work is supported by the National Natural Science Foundation of China (11871076)

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Abstract

This paper focuses on the quasi sure exponential stabilization of nonlinear systems. By virtue of exponential martingale inequality under $ G $-framework and intermittent $ G $-Brownian motion (in short, $ G $-ISSs), we establish the sufficient conditions to guarantee quasi surely exponential stability. The efficiency of the proposed results is illustrated by the memristor-based Chua's oscillator.

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Mathematics Subject Classification: Primary: 34A37, 60H10; Secondary: 34D10.

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