Global Exponential Stability of Commutative Quaternion-Valued Neural Networks With Time Varying Delays

The global exponential stability of commutative quaternion-valued neural networks (CQVNNs) with time varying delays is investigated in this paper. Considering that the Schwartz triangle inequality is not satisfied in the commutative quaternion field, the CQVNNs are isolated into real-valued neural networks by commutative multiplication rules among the three imaginary units. From the perspective of algebra and matrices, several sufficient conditions for ensuring the stability of CQVNNs are derived via the Lyapunov stability theory, the method of matrix measures and some inequality techniques. Finally, the feasibility and validity of the obtained outcomes are confirmed by an example.