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Discrete-time zeroing neural network for solving time-varying Sylvester-transpose matrix inequation via exp-aided conversion

Yunong Zhang, Yihong Ling, Shuai Li Orcid Logo, Min Yang, Ning Tan

Neurocomputing, Volume: 386, Pages: 126 - 135

Swansea University Author: Shuai Li Orcid Logo

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Abstract

Time-varying linear matrix equations and inequations have been widely studied in recent years. Time-varying Sylvester-transpose matrix inequation, which is an important variant, has not been fully investigated. Solving the time-varying problem in a constructive manner remains a challenge. This study...

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Published in: Neurocomputing
ISSN: 0925-2312
Published: Elsevier BV 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa53117
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Abstract: Time-varying linear matrix equations and inequations have been widely studied in recent years. Time-varying Sylvester-transpose matrix inequation, which is an important variant, has not been fully investigated. Solving the time-varying problem in a constructive manner remains a challenge. This study considers an exp-aided conversion from time-varying linear matrix inequations to equations to solve the intractable problem. On the basis of zeroing neural network (ZNN) method, a continuous-time zeroing neural network (CTZNN) model is derived with the help of Kronecker product and vectorization technique. The convergence property of the model is analyzed. Two discrete-time ZNN models are obtained with the theoretical analyses of truncation error by using two Zhang et al.’s discretization (ZeaD) formulas with different precision to discretize the CTZNN model. The comparative numerical experiments are conducted for two discrete-time ZNN models, and the corresponding numerical results substantiate the convergence and effectiveness of two ZNN discrete-time models.
Keywords: Zeroing neural network, Time-varying Sylvester-transpose matrix inequation, ZeaD formula, Discrete-time model, Exp-aided conversion
Start Page: 126
End Page: 135