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2021•2021 60th IEEE Conference on Decision and Control (CDC)Open access

An algorithm for J-spectral factorization of certain matrix functions

Lasha Ephremidze, Ilya M. Spitkovsky

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Abstract

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.

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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–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.

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Available abstract

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.

Key concepts: Matrix decomposition, Factorization, Spectral theorem, Algorithm, Block matrix, Matrix (chemical analysis), Mathematics, Incomplete LU factorization

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