Spectral and inner-outer factorizations of rational matrices
Spectral factorization and inner-outer factorization are basic techniques in treating many problems in electrical engineering. In this paper, the roblems of doing spectral and inner-outer factorizations via state-space methods are studied when the matrix to be factored is real-rational and surjectiv...
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Veröffentlicht in: | SIAM journal on matrix analysis and applications 1989, Vol.10 (1), p.1-17 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Spectral factorization and inner-outer factorization are basic techniques in treating many problems in electrical engineering. In this paper, the roblems of doing spectral and inner-outer factorizations via state-space methods are studied when the matrix to be factored is real-rational and surjective on the extended maginary axis. It is shown that our factorization problems can be reduced to solving a certain constrained Riccati equation, and that by examining some invariant ubspace of the associated Hamiltonian matrix there exists a unique solution to this equation. Finally, a state-space procedure to perform the factorization is proposed. |
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ISSN: | 0895-4798 1095-7162 |
DOI: | 10.1137/0610001 |