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

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.