Robust analysis of discrete time noises for stochastic systems and application in neural networks

ABSTRACT

Robust analysis in the stochastic sense, including robust boundedness and robust stability, has become a momentous problem of stochastic systems. Up to now, almost all existing works about robust boundedness and robust stability require that stochastic perturbations are rooted in continuous time observations of systems states. However, compared with the continuous time noises case, stochastic perturbations of discrete time noises are not only appropriate but also reasonable. Hence, this brief proposes and explores the problems of robust boundedness and robust stability of discrete time noises for stochastic systems satisfying the linear growth condition. The destination of this brief is to answer the question: how much stochastic perturbations of discrete time noises can a bounded or stable system tolerate guaranteeing stochastically perturbed system remains asymptotically bounded or stable. In addition, this brief discusses the application of our results in neural networks.

KEYWORDS:

• Stochastic delay differential systems
• discrete time noises
• Itô's formula
• robust boundedness
• robust stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project is jointly supported by the National Natural Science Foundation of China (NSFC) [grant numbers 11571024, 61833005, 61573096, 61773152 and 6127253], China Postdoctoral Science Foundation [grant numbers 2017M621588 and 2017T100318], Jiangsu Provincial Key Laboratory of Networked Collective Intelligence [grant number BM2017002], Science and Technology Research Foundation of Higher Education Institutions of Hebei Province of China [grant numbers QN2017116, Z2017014].