Global μ-stability of quaternion-valued neural networks with mixed time-varying delays

In this paper, the problem of global mu-stability for quaternion-valued neural networks with time-varying delays and unbounded distributed delays is investigated. To avoid the non-commutativity of quaternion multiplication, the quaternion-valued neural networks is decomposed into two complex-valued systems. By employing the homomorphic mapping principle, a sufficient condition for the existence and uniqueness of equilibrium point of the considered quaternion-valued neural networks is proposed in the form of linear matrix inequality (LMI) in complex-valued domain. Further, the appropriate Lyapunov-Krasovkii functional is constructed in the Hermitian quadratic form, and sufficient condition to ensure the global mu-stability of the equilibrium point is obtained by using inequality technique. Finally, two numerical examples with simulations are provided to verify the effectiveness of the obtained results. (c) 2018 Elsevier B.V. All rights reserved.