L∞-Norm Computation for Continuous-Time Descriptor Systems Using Structured Matrix Pencils

被引：33
作者：
Benner, Peter [1 ]
Sima, Vasile [2 ]
Voigt, Matthias [1 ]
机构：
[1] Max Planck Inst Dynam Complex Tech Syst, D-39106 Magdeburg, Germany
[2] Natl Inst Res & Dev Informat, Adv Res Dept, Bucharest 011455, Romania
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2012年 / 57卷 / 01期
关键词：
Continuous time systems; H-infinity control; numerical stability; singular systems; skew-Hamiltonian/Hamiltonian matrix pencils; transfer function matrices; ALGORITHM; EQUATION;
D O I：
10.1109/TAC.2011.2161833
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 technical note, we discuss an algorithm for the computation of the L-infinity-norm of transfer functions related to descriptor systems. We show how one can achieve this goal by computing the eigenvalues of certain skew-Hamiltonian/Hamiltonian matrix pencils and analyze arising problems. We also formulate and prove a theoretical result which serves as a basis for testing a transfer function matrix for properness. Finally, we illustrate our results using a descriptor system related to mechanical engineering.
引用
收藏
页码：236 / 241
页数：7
相关论文
共 26 条
[1]  
[Anonymous], 1989, LECT NOTES CONTROL I
[2]  
[Anonymous], THESIS TU BERLIN BER
[3]  
BENNER P, 1999, NUMERICAL COMPUTATIO
[4]   Computing rank-revealing QR factorizations of dense matrices [J].
Bischof, CH ;
Quintana-Ortí, G .
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1998, 24 (02) :226-253
[5]  
Boyd S., 1989, Mathematics of Control, Signals, and Systems, V2, P207, DOI 10.1007/BF02551385
[6]   A REGULARITY RESULT FOR THE SINGULAR-VALUES OF A TRANSFER-MATRIX AND A QUADRATICALLY CONVERGENT ALGORITHM FOR COMPUTING ITS L-INFINITY-NORM [J].
BOYD, S ;
BALAKRISHNAN, V .
SYSTEMS & CONTROL LETTERS, 1990, 15 (01) :1-7
[7]   A FAST ALGORITHM TO COMPUTE THE H-INFINITY-NORM OF A TRANSFER-FUNCTION MATRIX [J].
BRUINSMA, NA ;
STEINBUCH, M .
SYSTEMS & CONTROL LETTERS, 1990, 14 (04) :287-293
[8]   A BISECTION METHOD FOR MEASURING THE DISTANCE OF A STABLE MATRIX TO THE UNSTABLE MATRICES [J].
BYERS, R .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1988, 9 (05) :875-881
[9]  
Byers R., 2007, NUMERICAL SOLUTION R
[10]  
CHAHLAOUI Y, 2007, P ESAIM RAB ALG OCT, V20, P83
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