International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 45, Pages 2873-2885

Algorithm of J-factorization of rational matrices with zeros and poles on the imaginary axis

Vladimir B. Larin

Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov Street, Kiev, 03057, Ukraine

Received 27 October 2002

Copyright © 2003 Vladimir B. Larin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of J-factorization of rational matrices, which have zeros and poles on the imaginary axis, is reduced to construction of the solutions of two algebraic Riccati equations. For construction of these solutions, it is offered to use appropriate algorithms. These algorithms permit to find the solutions in cases when the Hamiltonian matrices, which are corresponding to these equations, have eigenvalues on the imaginary axis. Algorithms of factorization, which had been offered, permit to find the solution of the problem when the matrix, which will be factored, has zeros at infinity.