WebTo prove the existence of polynomial matrix spectral factorization, we begin with the rational polynomial matrix Cholesky Decomposition and modify it to remove lower half plane singularities. Namely given with each entry a complex coefficient polynomial we have rational polynomial matrix with for real , where has no lower half plane poles. Web18 de jun. de 2015 · Abstract: In this paper, we consider an arbitrary matrix-valued, rational spectral density Φ(z). We show with a constructive proof that Φ(z) admits a factorization of the form Φ(z)=W T (z -1) W(z), where W(z) is stochastically minimal.Moreover, W(z) and its right inverse are analytic in regions that may be selected with the only constraint that …

Correction to

WebIn this paper a novel theory and algorithm for spectral factorization is presented. It is … WebAbstract: The series connection \Sigma_{12} linear time-invariant systems \Sigma_1 and \Sigma_2 that have minimal state space system descriptions is considered. From these descriptions strict system equivalent polynomial matrix system descriptions in the manner of Rosenbrock are derived. They are based on the factorization of the transfer matrix of … fise itrack

On the factorization of rational matrices

Web1 de nov. de 1987 · In 1961 Youla published his paper “On the factorization of rational … WebThe results of these research usually depend on the existence of the LU factorization of a non-sigular matrix A, such that A = LU. Besides, in the most of the papers, or it is assumed that the matrix is invertible [2,6,10,16] or the conditions that ensure the nonsingularity of A and its LU factorization are not promptly obtained [7,8]. WebIn this paper, the roblems of doing spectral and inner-outer factorizations via state-space methods are studied when the matrix to be factored is real-rational and surjective on the extended maginary axis. fise it computer list