Abstract.
In this paper new algorithms are developed for J-spectral factorization of polynomial matrices. These algorithms are based on the calculus of two-variable polynomial matrices and associated quadratic differential forms, and share the common feature that the problem is lifted from the original one-variable polynomial context to a two-variable polynomial context. The problem of polynomial J-spectral factorization is thus reduced to a problem of factoring a constant matrix obtained from the coefficient matrices of the polynomial matrix to be factored. In the second part of the paper, we specifically address the problem of computing polynomial J-spectral factors in the context of H ∞ control. For this, we propose an algorithm that uses the notion of a Pick matrix associated with a given two-variable polynomial matrix.
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Date received: January 1, 1998. Date revised: October 15, 1998.
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Trentelman, H., Rapisarda, P. New Algorithms for Polynomial J-Spectral Factorization. Math. Control Signals Systems 12, 24–61 (1999). https://doi.org/10.1007/PL00009844
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DOI: https://doi.org/10.1007/PL00009844