Global Exponential Stability Analysis of Commutative Quaternion-Valued Neural Networks with Time Delays on Time Scales

In order to avoid the non-commutativity multiplication of quaternion, the commutative quaternion-valued neural networks (CQVNNs) with time delays are established on time scales, which can bring two different forms of discrete-time and continuous-time CQVNNs into a single framework. First, CQVNNs will be transformed into two complex-valued neural networks via the multiplication rules of commutative quaternion. Then, different sufficient criteria for global exponential stability of CQVNNs are studied mainly by employing matrix measure and some inequalities on time scales. Finally, two numerical examples will be used to verify the feasibility and validity for the achieved consequences.

Automated summary

In order to address the non-commutativity multiplication issue of quaternions, this study proposes the establishment of commutative quaternion-valued neural networks (CQVNNs) with time delays on time scales. By applying the multiplication rules of commutative quaternion, CQVNNs are transformed into two complex-valued neural networks, thereby combining discrete-time and continuous-time CQVNNs in a unified framework. Furthermore, sufficient criteria for the global exponential stability of CQVNNs are investigated using matrix measure and inequalities on time scales. Finally, the feasibility and validity of the obtained results are verified through two numerical examples.