On a Schur-algorithm approach to spectral factorization: state-space formulae

Abstract In some earlier publications [10–13] we indicated how the classical Schur algorithm can be used as a method to solve a spectral factorization problem. In the present paper indicate how to obtain a state-space formulation of the theory and formulae for an iterative algorithm for spectral factorization using state-space representations.

[1]  Tryphon Georgiou,et al.  Computational aspects of spectral factorization and the tangential Schur algorithm , 1987, 26th IEEE Conference on Decision and Control.

[2]  P. Dewilde,et al.  Lossless chain scattering matrices and optimum linear prediction: The vector case , 1981 .

[3]  Y. Kamp,et al.  The Nevanlinna–Pick Problem for Matrix-Valued Functions , 1979 .

[4]  Brian D. O. Anderson,et al.  Recursive algorithm for spectral factorization , 1974 .

[5]  B. Francis,et al.  A Course in H Control Theory , 1987 .

[6]  C. Foias,et al.  Harmonic Analysis of Operators on Hilbert Space , 1970 .

[7]  Patrick Dewilde,et al.  Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences , 1981, IEEE Trans. Inf. Theory.

[8]  T. Kailath A Theorem of I. Schur and Its Impact on Modern Signal Processing , 1986 .

[9]  J. Jeek,et al.  Paper: Efficient algorithm for matrix spectral factorization , 1985 .

[10]  Francois Germain,et al.  Opérateurs rationnels positifs : application à l'hyperstabilité et aux processus aléatoires , 1979 .

[11]  Vladimír Kucera,et al.  Discrete linear control: The polynomial equation approach , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  W. Tuel Computer algorithm for spectral factorization of rational matrices , 1968 .

[13]  J. Rissanen,et al.  1972 IFAC congress paper: Partial realization of random systems , 1972 .

[14]  Y. Kamp,et al.  Schur Parametrization of Positive Definite Block-Toeplitz Systems , 1979 .

[15]  F. Callier On polynomial matrix spectral factorization by symmetric extraction , 1985 .

[16]  Tryphon T. Georgiou,et al.  Spectral factorization and Nevanlinna-Pick interpolation , 1987 .

[17]  Tryphon T. Georgiou,et al.  Linear fractional transformations and spectral factorization , 1986 .

[18]  M. Vidyasagar Control System Synthesis : A Factorization Approach , 1988 .

[19]  Y. Genin,et al.  On the role of the Nevanlinna–Pick problem in circuit and system theory† , 1981 .

[20]  I. Schur,et al.  On Power Series Which are Bounded in the Interior of the Unit Circle II , 1986 .

[21]  Tryphon T. Georgiou,et al.  Spectral factorization of matrix-valued functions using interpolation theory , 1989 .

[22]  A. Laub A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.