Global $\mu$ -Stability of Quaternion-Valued Neural Networks With Unbounded and Asynchronous Time-Varying Delays

Abstract

In this paper, we investigate the global μ-stability problem of quaternion-valued neural networks (QVNNs) with unbounded and asynchronous time-varying delays. The decomposition of QVNNs is proposed first based on the Hamilton rules to avoid the non-communicative multiplication feature of the quaternion. Instead of establishing the Lyapunov-Krasovskii functional in the form of the Hermitian matrix, we combine the {ξ, ∞}-norm and the Cauchy convergence principle to derive the sufficient conditions that guarantee the existence, uniqueness, and μ-stability of the equilibrium point. The obtained criteria here are milder, owing to the consideration of inhibitory and excitatory between neurons. Finally, a specified example is presented to verify the correctness of the obtained results.