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Stability Analysis of High-order Proportional Delayed Cellular Neural Networks with D Operators

Xiaojin Guo, Chuangxia Huang, Zhichun Yang*, Jiping Zhang, and Jinde Cao
International Journal of Control, Automation, and Systems, vol. 20, no. 2, pp.660-668, 2022

Abstract : In this paper, we focus on a class of high-order proportional delayed cellular neural networks involving D operator. First of all, the existence on the positive equilibrium points of the addressed system is revealed by applying the Brouwer’s fixed point theorem. Secondly, by utilizing the differential inequality techniques, Lyapunov function method and the matrix spectral radius theory, the global exponential stability of the positive equilibrium point is established for the first time, which shows that all solutions of the addressed system are eventually positive. Finally, the validity and practicability of our results are illustrated by some numerical simulations. The obtained results extend and improve some existing ones.

Keyword : D operator, high-order neural networks, positive equilibrium point, proportional delay, stability.

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