Robust Stability of Quaternion-Valued Neural Networks with Multiple Time Delays and Parameter Uncertainty

In this paper, a non-decomposition approach is adopted to study the robust stability of quaternion-valued neural networks (QVNNs) with leakage, discrete, and neutral time delays, and the parameter uncertainty is also considered. The existence and uniqueness of the equilibrium of QVNNs are proved by the homogeneous mapping theorem. By constructing appropriate Lyapunov functions and employing quaternion modulus inequality techniques, sufficient conditions for the global robust stability of QVNNs are presented. Notably, the considered QVNN is treated as a whole rather than being decomposed into complex-valued neural networks (CVNNs) or real-valued neural networks (RVNNs), which faithfully reflects the internal connections between quaternion neurons. Two numerical examples are used to verify the validity of the obtained conclusions.