Parametric solutions to the regulator-conjugate matrix equations

Lei Zhang; Anfu Zhu; Aiguo Wu; Lingling Lv

doi:10.3934/jimo.2016036

Article Contents

2017, Volume 13, Issue 2: 623-631. Doi: 10.3934/jimo.2016036

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Parametric solutions to the regulator-conjugate matrix equations

1.
Institute of Data and Knowledge Engineering, Henan University, Kaifeng 475004, China
2.
Institute of electric power, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
3.
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China

* Corresponding author: Lingling Lv
* Corresponding author: Lingling Lv

Received: August 2015

Revised: December 2015

Published: August 2017

This work is supported by the Programs of National Natural Science Foundation of China (Nos. 61402149,11501200, U1604148), Innovative Talents of Higher Learning Institutions of Henan (No. 17HASTIT023), Program for Innovative Research Team in University of Henan Province (No. 16IRTSTHN017).

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Abstract

The problem of solving regulator-conjugate matrix equations is considered in this paper. The regulator-conjugate matrix equations are a class of nonhomogeneous equations. Utilizing several complex matrix operations and the concepts of controllability-like and observability-like matrices, a special solution to this problem is constructed, which includes solving an ordinary algebraic matrix. Combined with our recent results on Sylvester-conjugate matrix equations, complete solutions to regulator-conjugate matrix equations can be obtained by superposition principle. The correctness and effectiveness are verified by a numerical example.

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Mathematics Subject Classification: 15A24.

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