Explicit solutions of conjugate, periodic, time-varying Sylvester equations

Journal of Inequalities and Applications

Research

Mengqi Han¹  Rui Chang²  Yongmei Jiao³  Li Ma³ 

[1] Baoyuan Industrial Investment Co., Ltd., 464200, Xinyang, China;College of Electrical Engineering, North China University of Water Resources and Electric Power, 450046, Zhengzhou, China;Department of Electrical Engineering, Shijiazhuang Tiedao University Sifang College, 050043, Shijiazhuang, China;

关键词: Explicit solutions;    Conjugate;    Time-varying matrix equations;    Quasicontrollability matrix;    Conjugate operations;    Real representation;   

DOI  :  10.1186/s13660-023-03048-3

 received in 2023-08-21, accepted in 2023-10-10,  发布年份 2023

来源: Springer

【 摘 要 】

Solutions of a group of conjugate time-varying matrix equations are discussed in this paper. Through mathematical derivation, the solutions to this group of equations are equivalent to the solutions to a class of conjugate time-invariant matrix equations. Further, the related conditions of solvability are obtained and the general explicit solutions are represented by using quasicontrollability and quasiobservability matrices. A detailed algorithm is presented to make the calculation process clear, and the effectiveness of the algorithm is verified by a concrete example. The proposed algorithm can provide complete solutions to the considered equation in explicit parametric form and its main computation includes solving an ordinary linear algebraic equation and some matrix multiplication operations.

【 授权许可】

CC BY   
© Springer Nature Switzerland AG 2023

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