Stability-preserving parametric model reduction by matrix interpolation

被引：14

作者：

Eid, Rudy ^{[1
]}

Castane-Selga, Rosa ^{[1
]}

Panzer, Heiko ^{[1
]}

Wolf, Thomas ^{[1
]}

Lohmann, Boris ^{[1
]}

机构：

[1] Tech Univ Munich, Inst Automat Control, D-85748 Garching, Germany

来源：

MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS | 2011年 / 17卷 / 04期

关键词：

parametric model order reduction; stability preservation; contractivity; port-Hamiltonian systems; RANK SMITH METHOD; BALANCED TRUNCATION; ORDER REDUCTION; PASSIVITY; SYSTEMS; NORMS;

D O I：

10.1080/13873954.2011.547671

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this article, a method to preserve stability in parametric model reduction by matrix interpolation is presented. Based on the matrix measure approach, sufficient conditions on the original system matrices are derived. Once they are fulfilled, the stability of each of the reduced models is guaranteed as well as that of the parametric model resulting from interpolation. In addition, it is shown that these sufficient conditions are met by port-Hamiltonian systems and by a relevant set of second-order systems obtained by the finite element method. The new approach is illustrated by two numerical examples.

引用

页码：319 / 335

页数：17

共 36 条

[31] LOGARITHMIC NORMS [J].

STROM, T .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1975, 12 (05) :741-753

[32]

Van Der Lee A. M., 2000, Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504), DOI 10.1109/IQEC.2000.907797

[33]

Villemagne C.E., 1987, International Journal of Control, V46, P2141

[34] A method for generating rational interpolant reduced order models of two-parameter linear systems [J].

Weile, DS ;

Michielssen, E ;

Grimme, E ;

Gallivan, K .

APPLIED MATHEMATICS LETTERS, 1999, 12 (05) :93-102

[35] Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces [J].

Wolf, Thomas ;

Lohmann, Boris ;

Eid, Rudy ;

Kotyczka, Paul .

EUROPEAN JOURNAL OF CONTROL, 2010, 16 (04) :401-406

[36]

Yousefi A., 2006, THESIS TU MUNCHEN

← 1 2 3 4 →