Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field.

Zhang, Dandan; Kou, Kit Ian; Liu, Yang; Cao, Jinde · Neural Netw · 2017

basic_science · Level V

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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=i<sup>2</sup>=j<sup>2</sup>=k<sup>2</sup>=-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.

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