Two finite-time convergent Zhang neural network models for time-varying complex matrix Drazin inverse

This paper concerns the computation of the Drazin inverse of a complex time-varying matrix. Based on two Zhang functions constructed from two limit representations of the Drazin inverse, we present two complex Zhang neural network (ZNN) models with the Li activation function for computing the Drazin...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 542; pp. 101 - 117
Main Authors Qiao, Sanzheng, Wang, Xue-Zhong, Wei, Yimin
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.04.2018
American Elsevier Company, Inc
Subjects
Complex neural network
Computer simulation
Convergence
Drazin inverse
Li function
Linear algebra
Mathematical functions
Matrix
Neural networks
Time-varying complex matrix
Upper bounds
Drazin inverse
65F20
Li function
Time-varying complex matrix
15A09
Complex neural network
Convergence
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Summary:This paper concerns the computation of the Drazin inverse of a complex time-varying matrix. Based on two Zhang functions constructed from two limit representations of the Drazin inverse, we present two complex Zhang neural network (ZNN) models with the Li activation function for computing the Drazin inverse of a complex time-varying square matrix. We prove that our ZNN models globally converge in finite time. In addition, upper bounds of the convergence time are derived analytically via the Lyapunov theory. Our simulation results verify the theoretical analysis and demonstrate the superiority of our ZNN models over the gradient-based GNN models.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.03.014