Article ID Journal Published Year Pages File Type
4946647 Neural Networks 2017 35 Pages PDF
Abstract
In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij=−ji=k, jk=−kj=i, ki=−ik=j, ijk=i2=j2=k2=−1, the QVNN is decomposed into four real-valued systems, which are studied separately. The exponential convergence is proved directly accompanied with the existence and uniqueness of the equilibrium point to the consider systems. Combining with the generalized ∞-norm and Cauchy convergence property in the quaternion field, some sufficient conditions to guarantee the stability are established without using any Lyapunov-Krasovskii functional and linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the results.
Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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