An algorithm for J-spectral factorization of certain matrix functions

TL;DR

This paper introduces a numerical algorithm for J-spectral factorization of certain matrix functions, extending existing spectral factorization methods to indefinite cases relevant for MIMO control systems.

Contribution

The paper presents a novel numerical algorithm for J-spectral factorization applicable to matrices with constant signatures, expanding the Janashia-Lagvilava method to indefinite matrices.

Findings

Algorithm successfully performs J-spectral factorization on test matrices.

Extends spectral factorization techniques to indefinite matrix cases.

Numerical example demonstrates practical applicability.

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 principle submatrices. A numerical example is presented for illustrative purposes.