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Rational spectral factorization using state-space methods. (English) Zbl 0772.93002
Summary: We describe a state-space-based algorithm to find the minimum phase spectral factor of any rational spectral density, whether it be proper, improper, or polynomial.

##### MSC:
 93A10 General systems
##### Keywords:
spectral factorization; rational spectral density
RICPAC
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##### References:
 [1] Arnold, W.F.; Laub, A.J., Generalized eigenproblem algorithms and software for algebraic Riccati equations, (), 1746-1754 [2] Callier, F.M., On polynomial matrix spectral factorization by symmetric extraction, IEEE trans. automat. control, AC30, 453-464, (1985) · Zbl 0556.65034 [3] Clements, D.J., Improper spectral factorization and linear-quadratic control for descriptor systems, UNSW tech. report, (1989) [4] Clements, D.J.; Anderson, B.D.O., Singular optimal control: the linear-quadratic problem, () · Zbl 0348.49003 [5] Clements, D.J.; Glover, K., Spectral factorization by Hermitian pencils, Linear algebra appl., 122-124, 797-846, (1989) · Zbl 0678.93006 [6] Grimm, J., Realization and canonicity for implicit systems, SIAM J. control optim., 26, 1331-1347, (1988) · Zbl 0666.93018 [7] Hammerling, S.J.; Singer, M.A., A. canonical form for the algebraic Riccati equation, () · Zbl 0531.93017 [8] Laub, A.J., A Schur method for solving algebraic Riccati equations, IEEE trans. automat. control, AC24, 913-925, (1979) · Zbl 0424.65013 [9] Singer, M.A.; Hammarling, S.J., The algebraic Riccati equation: a summary of some available results, NPL report, 23, (1983) [10] Van Dooren, P., A generalized eigenvalue approach for solving Riccati equations, SIAM J. sci. stat. comput., 2, 121-135, (1981) · Zbl 0463.65024 [11] Y.Y. Wang, P.M. Frank, and D.J. Clements, Gain and phase margins for LQ regulators for singular systems, IEEE Trans. Automat. Control, to appear. [12] Youla, D.C., On the factorization of rational matrices, IRE trans. inform. theory, IT7, 172-189, (1961) · Zbl 0103.25201
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