Abstract:
In this paper, we investigate the global stability of quaternion-valued neural networks (QVNNs) with time-varying delays. On one hand, in order to avoid the noncommutativ...Show MoreMetadata
Abstract:
In this paper, we investigate the global stability of quaternion-valued neural networks (QVNNs) with time-varying delays. On one hand, in order to avoid the noncommutativity of quaternion multiplication, the QVNN is decomposed into four real-valued systems based on Hamilton rules: ij = - ji = k, jk = -kj = i, ki = -ik = j, i2 = j2 = k2 = ijk = -1. With the Lyapunov function method, some criteria are, respectively, presented to ensure the global μ-stability and power stability of the delayed QVNN. On the other hand, by considering the noncommutativity of quaternion multiplication and time-varying delays, the QVNN is investigated directly by the techniques of the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) where quaternion self-conjugate matrices and quaternion positive definite matrices are used. Some new sufficient conditions in the form of quaternion-valued LMI are, respectively, established for the global μ-stability and exponential stability of the considered QVNN. Besides, some assumptions are presented for the two different methods, which can help to choose quaternion-valued activation functions. Finally, two numerical examples are given to show the feasibility and the effectiveness of the main results.
Published in: IEEE Transactions on Neural Networks and Learning Systems ( Volume: 29, Issue: 9, September 2018)