Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

Abstract

In this paper, a general setting is presented to study the exponential stability of discrete-time systems with bounded or unbounded delays. Based on the M-matrix theory, we establish sufficient conditions to ensure the global exponential stability of the zero equilibrium of low-order, and high-order, discrete-time Hopfield neural network models with unbounded delays and delay in the leakage terms. A comparison of the literature shows that our results generalize and improve some in recent publications.

Keywords:

• Neural networks
• delay difference equations
• unbounded delays
• global stability

2020 Mathematics Subject Classifications:

• 39A30
• 39A60
• 92B20

Acknowledgments

The author expresses his gratitude to the referees for their valuable comments and suggestions.

Disclosure statement

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

Additional information

Funding

The research was partially financed by Portuguese Funds through FCT (Fundação para a Ciência e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020.