Open AccessOn the solutions to Sylvester‐conjugate periodic matrix equations via iteration
Author(s) -
Zhang Lei,
Li Pengxiang,
Han Mengqi,
Zhang Yanfeng,
Chang Rui,
Zhang Jinhua
Publication year - 2023
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12312
Subject(s) - sylvester equation , sylvester matrix , sylvester's law of inertia , mathematics , matrix (chemical analysis) , conjugate gradient method , control theory (sociology) , mathematical optimization , computer science , mathematical analysis , symmetric matrix , artificial intelligence , physics , control (management) , materials science , eigenvalues and eigenvectors , matrix polynomial , quantum mechanics , polynomial matrix , polynomial , composite material
The problem of solving a class of Sylvester‐conjugate periodic matrix equations is investigated in this paper. Utilising conjugate gradient method, an iterative algorithm is provided, from which a matrix sequence can be generated to approximate the unknown matrix of the equation to be solved. Theoretical derivation proves that the proposed algorithm is convergent starting from any initial value, and simulation examples show the effectiveness of the proposed algorithm.