Schur complements and state space realizations

被引：18
|
作者：
Bart, H
Gohberg, I
Kaashoek, MA
Ran, ACM
机构：
[1] Erasmus Univ, Inst Econometr, NL-3000 DR Rotterdam, Netherlands
[2] Tel Aviv Univ, Sch Math Sci, Raymond & Beverly Sackler Fac Exact Sci, Ramat Aviv, Israel
[3] Vrije Univ Amsterdam, Dept Math, FEW, NL-1081 HV Amsterdam, Netherlands
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 399卷
关键词：
equivalence; extension; factorization; realization; Schur complement; transfer function;
D O I：
10.1016/j.laa.2004.10.027
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Motivated by state space realizations of transfer functions from system theory, a number of operations on Schur complements are introduced and studied. These operations are equivalence, extension, multiplication, inversion, and factorization. Together they form an algebraic framework which is of independent interest, and also useful in solving problems in analysis. (c) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：203 / 224
页数：22
相关论文
共 50 条
  • [21] The Schur algorithm for generalized Schur functions IV: Unitary realizations
    Alpay, D
    Azizov, TY
    Dijksma, A
    Langer, H
    Wanjala, G
    CURRENT TRENDS IN OPERATOR THEORY AND ITS APPLICATIONS, 2004, 149 : 23 - 45
  • [22] The Schur algorithm for generalized Schur functions I: coisometric realizations
    Alpay, D
    Azizov, T
    Dijksma, A
    Langer, H
    SYSTEMS, APPROXIMATION, SINGULAR INTEGRAL OPERATORS, AND RELATED TOPICS, 2001, 129 : 1 - 36
  • [23] The Schur Algorithm in Terms of System Realizations
    Fritzsche, Bernd
    Katsnelson, Victor
    Kirstein, Bernd
    CHARACTERISTIC FUNCTIONS, SCATTERING FUNCTIONS AND TRANSFER FUNCTIONS: THE MOSHE LIVSIC MEMORIAL VOLUME, 2010, 197 : 181 - +
  • [24] COMPLEMENTS TO COST-EQUIVALENT REALIZATIONS
    FRAZHO, AE
    SKELTON, RE
    WAGIE, DA
    INTERNATIONAL JOURNAL OF CONTROL, 1984, 40 (05) : 1045 - 1048
  • [25] Generalized Schur–Nevanlinna functions and their realizations
    Lassi Lilleberg
    Integral Equations and Operator Theory, 2020, 92
  • [26] On state-space realizations of composition of functions
    Flores-Godoy, José-Job
    Fernández-Anaya, Guillermo
    WSEAS Transactions on Circuits and Systems, 2007, 6 (03): : 310 - 315
  • [27] Generalized Schur complements and oblique projections
    Corach, G
    Maestripieri, A
    Stojanoff, D
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 341 : 259 - 272
  • [28] Some inequalities on generalized Schur complements
    Wang, BY
    Zhang, XP
    Zhang, FZ
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 303 : 163 - 172
  • [29] Pseudo-Schur complements and their properties
    Redivo-Zaglia, M
    APPLIED NUMERICAL MATHEMATICS, 2004, 50 (3-4) : 511 - 519
  • [30] Observable state space realizations for multivariable systems
    Gu, Ya
    Ding, Ruifeng
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (09) : 1389 - 1399
12345