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

[11] Gantmacher F. R., 1959, THEORY MATRICES, V2
[12] ALL OPTIMAL HANKEL-NORM APPROXIMATIONS OF LINEAR-MULTIVARIABLE SYSTEMS AND THEIR L INFINITY-ERROR BOUNDS
GLOVER, K
[J]. INTERNATIONAL JOURNAL OF CONTROL, 1984, 39 (06) : 1115 - 1193
[13] Grimme E. J., 1997, Krylov projection methods for model reduction
[14] Model reduction of state space systems via an implicitly restarted Lanczos method
Grimme, EJ
Sorensen, DC
VanDooren, P
[J]. NUMERICAL ALGORITHMS, 1996, 12 (1-2) : 1 - 31
[15] A survey of model reduction by balanced truncation and some new results
Gugercin, S
Antoulas, AC
[J]. INTERNATIONAL JOURNAL OF CONTROL, 2004, 77 (08) : 748 - 766
[16] Halevi Y, 2004, P AMER CONTR CONF, P113
[17] HALEVI Y, 2002, 15 IFAC WORLD C AUT, P6
[18] Implicitly restarted Krylov subspace methods for stable partial realizations
Jaimoukha, IM
Kasenally, EM
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1997, 18 (03) : 633 - 652
[19] KAGSTROM B, 1992, J NUMER LINEAR ALGEB, V1, P165
[20] Assigning the Kronecker invariants of a matrix pencil by row or column completions
Loiseau, JJ
Mondie, S
Zaballa, I
Zagalak, P
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 278 (1-3) : 327 - 336

← 1 2 3 →