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The problems of matrix spectral factorization and J-spectral factorization appear to be important for practical use in many MIMO control systems. We propose a numerical algorithm for J&#x2013;spectral factorization which extends Janashia&#x2013;Lagvilava matrix spectral factorization method to the indefinite case. The algorithm can be applied to matrices that have constant signatures for all leading principal submatrices. A numerical example is presented for illustrative purposes.

An algorithm for J-spectral factorization of certain matrix functions