A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

doi:10.1007/s10473-024-0320-y

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (3): 1145-1164.doi: 10.1007/s10473-024-0320-y

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Lichao Feng^1,*, Chunyan Zhang¹, Jinde Cao^3,4,*, Zhihui Wu⁵

1. College of Science, North China University of Science and Technology,Tangshan 063210, China;
2. School of Mathematics, Southeast University, Nanjing 210096, China;
3. Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea;
4. Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

收稿日期:2022-08-29 修回日期:2023-04-12 出版日期:2024-06-25 发布日期:2024-05-21

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Lichao Feng^1,*, Chunyan Zhang¹, Jinde Cao^3,4,*, Zhihui Wu⁵

1. College of Science, North China University of Science and Technology,Tangshan 063210, China;
2. School of Mathematics, Southeast University, Nanjing 210096, China;
3. Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea;
4. Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received:2022-08-29 Revised:2023-04-12 Online:2024-06-25 Published:2024-05-21
Contact: *Lichao Feng, E-mail:fenglichao19820520@163.com;Jinde Cao, E-mail:jdcao@seu.edu.cn
About author:Chunyan Zhang, zhang-chunyan3060@163.com;Zhihui Wu E-mail:wuzhihui@hrbust.edu.cn
Supported by:
National Natural Science Foundation of China (61833005), the Humanities and Social Science Fund of Ministry of Education of China (23YJAZH031), the Natural Science Foundation of Hebei Province of China (A2023209002, A2019209005) and the Tangshan Science and Technology Bureau Program of Hebei Province of China (19130222g).

摘要/Abstract

摘要： Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system (HNSDDS) under a highly nonlinear constraint %high nonlinearity, in the $H_{\infty}$ and exponential forms. Nevertheless, the existing work just adapted to autonomous cases, and the obtained results were mainly on exponential stabilization. In comparison with autonomous cases, non-autonomous systems are of great interest and represent an important challenge. Accordingly, discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS, in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted. It should be noted, in particular, that the stabilization can be achieved not only in the routine $H_{\infty}$ and exponential forms, but also the polynomial form and even a general form.

关键词: hybrid neutral stochastic differential delay system, discrete feedback control, general stabilization, polynomial stabilization

Abstract: Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system (HNSDDS) under a highly nonlinear constraint %high nonlinearity, in the $H_{\infty}$ and exponential forms. Nevertheless, the existing work just adapted to autonomous cases, and the obtained results were mainly on exponential stabilization. In comparison with autonomous cases, non-autonomous systems are of great interest and represent an important challenge. Accordingly, discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS, in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted. It should be noted, in particular, that the stabilization can be achieved not only in the routine $H_{\infty}$ and exponential forms, but also the polynomial form and even a general form.

Key words: hybrid neutral stochastic differential delay system, discrete feedback control, general stabilization, polynomial stabilization

中图分类号:

93D15

Lichao Feng, Chunyan Zhang, Jinde Cao, Zhihui Wu. A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY[J]. 数学物理学报(英文版), 2024, 44(3): 1145-1164.

Lichao Feng, Chunyan Zhang, Jinde Cao, Zhihui Wu. A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY[J]. Acta mathematica scientia,Series B, 2024, 44(3): 1145-1164.

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A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

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