Further research on exponential stability for quaternion-valued neural networks with mixed delays

Abstract

This paper addresses the global exponential stability of a class of quaternion-valued neural networks (QVNNs) with mixed delays including time-varying delays and infinite distributed delays. Because of the noncommutativity of quaternion multiplication, the concerned quaternion-valued models separated into four real-valued parts to form the equivalent real-valued systems. Based on M-matrix properties and homomorphism mapping theories, some sufficient conditions are derived to guarantee the existence and uniqueness of the equilibrium point of the system. Conditions for ensuring the global exponential stability of the equilibrium point of the system are obtained on the basis of the vector Lyapunov function method instead of the linear matrix inequality method. Using a similar method, the mixed-delay QVNNs with parameter uncertainties are also studied, and the conditions for ensuring the global robust exponential stability of the system are established directly. The adopted approach and the obtained results in this paper complement already the existing ones. Finally, three numerical examples are provided to illustrate the feasibility and the less level conservatism of the main results.