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

Yannan Xia, Xiaofeng Chen, Dongyuan Lin, Bing Li, Xujun Yang

Abstract: 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.