Spectral factorization and stochastic realization with zeros on the unit circle

We study the spectral factorization problem of a rational m/spl times/m spectral density matrix /spl Phi/(z) = /spl Phi/(z/sup -1/)/sup T/ which has zeros on the unit circle. In the control/estimation literature this situation is either excluded by assuming appropriate stabilizability and detectabil...

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Bibliographic Details
Published in42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) Vol. 2; pp. 1398 - 1403 Vol.2
Main Authors Ferrante, A., Picci, G., Pinzoni, S.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2003
Subjects
Eigenvalues and eigenfunctions
Estimation theory
H infinity control
Linear systems
Matrix decomposition
Riccati equations
Spectral analysis
Stochastic processes
Symmetric matrices
White noise
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Summary:We study the spectral factorization problem of a rational m/spl times/m spectral density matrix /spl Phi/(z) = /spl Phi/(z/sup -1/)/sup T/ which has zeros on the unit circle. In the control/estimation literature this situation is either excluded by assuming appropriate stabilizability and detectability conditions or is discussed only partially. Here we provide what seems to be a complete solution, at least in the full-rank case.
ISBN:9780780379244
0780379241
ISSN:0191-2216
DOI:10.1109/CDC.2003.1272805