On stability and synchronisation of coupled neural networks by vector distributed-order Halanay inequalities
Fengxian Wang, Xiaoyu Liang, Ruidong Chen, Xinge Liu · International Journal of Systems Science · 2025
This paper studies the stability and synchronisation of coupled heterogeneous vector distributed-order neural networks (HVDNNs) with unbounded delay. First, the classical fractional-order Halanay inequality is generalised to a vector distributed-order Halanay inequality through the utilisation of the final value theorem and the Laplace transformation of distributed-order derivatives. It is demonstrated that the vector distributed-order Halanay inequality is valid under a non-singular M-matrix condition. According to the M-matrix equivalence theorem, the non-singular M-matrix condition is equivalent to a linear matrix inequality (LMI), which can be solved by the LMI toolbox. Then, a LMI stability condition of coupled HVDNNs is obtained by employing the generalised inequality technique. Moreover, a dynamic event-triggered controller is designed to achieve synchronisation of coupled HVDNNs by incorporating the two-parameter Mittag–Leffler function into the threshold function of the dynamic event-triggered controller. The proposed method effectively excludes Zeno behaviour. Finally, three simulation examples are used to demonstrate the feasibility and effectiveness of the proposed methods.