On the Factorization of Rational Discrete-Time Spectral Densities

被引：18
|
作者：
Baggio, Giacomo [1 ]
Ferrante, Augusto [1 ]
机构：
[1] Univ Padua, Dipartimento Ingn Informaz, I-35131 Padua, Italy
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 04期
关键词：
Acausal estimation; LQ optimization; spectral factorization; stochastic realization; ALGEBRAIC RICCATI EQUATION; NEGATIVE-IMAGINARY SYSTEMS; H-INFINITY; MATRIX POLYNOMIALS; ALGORITHM; REALIZATIONS;
D O I：
10.1109/TAC.2015.2446851
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we consider an arbitrary matrix-valued, rational spectral density Phi(z). We show with a constructive proof that Phi(z) admits a factorization of the form Phi(z)=W-T (z(-1)) W(z), where W(z) is stochastically minimal. Moreover, W(z) and its right inverse are analytic in regions that may be selected with the only constraint that they satisfy some symplectic-type conditions. By suitably selecting the analyticity regions, this extremely general result particularizes into a corollary that may be viewed as the discrete-time counterpart of the matrix factorization method devised by Youla in his celebrated work [48].
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页码：969 / 981
页数：13
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