Boundedness theorems of discrete-time stochastic delay systems and applications to neural networks

Danhua He and Liguang Xu

International Journal of Systems Science, 2025, vol. 56, issue 15, 3702-3717

Abstract: This paper focuses on investigating the pth exponential ultimate boundedness of a class of discrete-time stochastic delay systems and its application in neural networks. By employing a novel method that combines inequality techniques and reductio ad absurdum, several sufficient conditions for the pth exponential ultimate boundedness of the addressed systems are derived. This method not only circumvents the hardship of constructing Lyapunov functional but also yields simpler criteria for exponential ultimate boundedness criteria. As applications, the criteria for boundedness are utilised in neural networks. Finally, the validity of the theoretical results is verified by numerical examples.

Date: 2025
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DOI: 10.1080/00207721.2025.2474717

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