Discrete-time feedback control of highly nonlinear hybrid stochastic neural networks with non-differentiable delays

Abstract

This paper investigates the stability of a class of highly nonlinear hybrid stochastic neural networks (HSNNs). Distinct from existing results, the system coefficients satisfy polynomial growth conditions instead of the usual linear growth conditions; the delays in the considered systems are time-varying delays with non-differentiable. In this paper, feedback control based on discrete-time state and mode observations is used to make the system stable. By applying the Lyapunov functional method, four results on the stabilisation of the controlled systems are established. Moreover, the upper bound on the duration τ between two consecutive state and mode observations is gained. At last, two examples are given to illustrate the validity of the theoretical results.

Keywords:

• Hybrid stochastic neural networks
• non-differentiable delays
• discrete-time feedback control
• stability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Natural Science Foundation of Hubei Province of China [grant number 2021CFA080] and the Young Top-Notch Talent Cultivation Program of Hubei Province of China.