On the embedding of state space realizations

被引：1

作者：

Genin, Yves ^{[1
]}

Vandendorpe, Antoine ^{[1
]}

机构：

[1] Catholic Univ Louvain, FSA, Fac Sci Appl, B-1348 Louvain, Belgium

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2007年 / 19卷 / 02期

关键词：

model order reduction; linear time invariant system; truncation technique; embedding; state space;

D O I：

10.1007/s00498-006-0011-3

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, the generality of the particular model reduction method, known as the projection of state space realization, is investigated. Given two transfer functions, one wants to find the necessary and sufficient conditions for the embedding of a state-space realization of the transfer function of smaller McMillan degree into a state-space realization of the transfer function of larger McMillan degree. Two approaches are considered, both in the MIMO case. First, when the difference of the McMillan degree between the transfer functions is equal to one and there is no common pole, necessary and sufficient conditions are provided. Then, the generic case is considered using a pencil approach. Finally, it is shown that the condition of embedding is related to the eigen structure of a pencil that appears in the framework of tangential interpolation.

引用

页码：123 / 149

页数：27

共 30 条

[1] [Anonymous], 2011, ADV NEURAL INFORM PR
[2] [Anonymous], 1980, LINEAR SYSTEMS INFOR
[3] Antoulas A.C., 2005, ADV DES CONTROL, DOI 10.1137/1.9780898718713
[4] ON THE PROBLEM OF STABLE RATIONAL INTERPOLATION
ANTOULAS, AC
ANDERSON, BDO
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 122 : 301 - 329
[5] CHAHLAOUI Y, 2004, P 16 S MATH THEOR NE
[6] DESA EM, 1979, LINEAR ALGEBRA APPL, V24, P33
[7] Krylov-subspace methods for reduced-order modeling in circuit simulation
Freund, RW
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 123 (1-2) : 395 - 421
[8] Model reduction of MIMO systems via tangential interpolation
Gallivan, K
Vandendorpe, A
Van Dooren, P
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2004, 26 (02) : 328 - 349
[9] Model reduction via truncation: an interpolation point of view
Gallivan, K
Vandendorpe, A
Van Dooren, P
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 375 : 115 - 134
[10] ASYMPTOTIC WAVE-FORM EVALUATION VIA A LANCZOS METHOD
GALLIVAN, K
GRIMME, E
VANDOOREN, P
[J]. APPLIED MATHEMATICS LETTERS, 1994, 7 (05) : 75 - 80

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