Decoupling of cubic polynomial matrix systems

Peizhao Yu; Guoshan Zhang; Yi Zhang

doi:10.3934/naco.2020012

Article Contents

2021, Volume 11, Issue 1: 13-26. Doi: 10.3934/naco.2020012

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Decoupling of cubic polynomial matrix systems

1.
School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
2.
School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China
3.
School of Science, Shenyang University of Technology, Shenyang 110870, China

^* Corresponding author: Guoshan Zhang, zhanggs@tju.edu.cn
^* Corresponding author: Guoshan Zhang, zhanggs@tju.edu.cn

Received: May 2019

Revised: October 2019

Early access: February 2020

Published: March 2021

The work is supported by the National Natural Science Foundation of China (grant NO. 61473202 and 61903342) and the Doctor fund project of Zhengzhou University of Light Industry (grant NO. 2017BSJJ009)

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Abstract

The decoupling of polynomial matrix system is to diagonalize its system matrix. In this paper, decoupling problems for cubic polynomial matrix system are considered. The decoupling conditions for a class of cubic polynomial matrix systems are derived under strict equivalence transformation. By using linearization, isospectral decoupling method for cubic polynomial matrix system is proposed. To be specific, necessary and sufficient conditions of isospectral diagonalization for nonsingular cubic polynomial matrix are given. These results are extended to singular cubic polynomial matrix. Solving processes are given to obtain isospectral diagonal cubic polynomial matrix for nonsingular and singular cases. Finally, illustrating examples are provided to verify the main results.

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Mathematics Subject Classification: Primary: 15A18, 15A21; Secondary: 65F15.

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