Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (3): 1145-1164.doi: 10.1007/s10473-024-0320-y

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

Lichao Feng1,*, Chunyan Zhang1, Jinde Cao3,4,*, Zhihui Wu5   

  1. 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).

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

CLC Number: 

  • 93D15
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