An algorithm for J-spectral factorization of certain matrix functions

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–spectral factorization which extends Janashia–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.