Controller reduction by balanced truncation for infinite-dimensional, discrete-time systems

被引：0

作者：

Selig, Tilman ^{[1
]}

机构：

[1] Tech Univ Ilmenau, Inst Math, D-98693 Ilmenau, Germany

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2015年 / 27卷 / 01期

关键词：

Balanced truncation; Controller reduction; H-infinity control; Infinite-dimensional discrete-time linear systems; Model reduction; REALIZATION;

D O I：

10.1007/s00498-014-0137-7

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider Lyapunov and balancing as well as model reduction by balanced truncation for infinite-dimensional, discrete-time linear systems. A functional analytic approach to state space transformation leading to balanced realization is presented. Furthermore, we show that a finite-dimensional controller designed for a balanced and truncated system stabilizes the original infinite-dimensional system, provided the error made by this model reduction procedure is small enough.

引用

页码：111 / 147

页数：37

共 24 条

[1]

[Anonymous], 1972, FUNCTIONAL ANAL METH

[2] An overview of approximation methods for large-scale dynamical systems [J].

Antoulas, AC .

ANNUAL REVIEWS IN CONTROL, 2005, 29 (02) :181-190

[3] CONVERGENCE AND CONVERGENCE RATE OF THE BALANCED REALIZATION TRUNCATIONS FOR INFINITE-DIMENSIONAL DISCRETE-TIME-SYSTEMS [J].

BONNET, C .

SYSTEMS & CONTROL LETTERS, 1993, 20 (05) :353-359

[4] AN L-INFINITY-CONVERGENT METHOD TO REDUCE FREQUENCY-WEIGHTED INFINITE-DIMENSIONAL DISCRETE-TIME-SYSTEMS [J].

BONNET, C .

SYSTEMS & CONTROL LETTERS, 1993, 21 (06) :443-450

[5]

CURTAIN RF, 1986, LECT NOTES CONTR INF, V84, P181

[6] Normalized H∞ controller reduction with A Priori error bounds [J].

El-Zobaidi, HMH ;

Jaimoukha, IM ;

Limebeer, DJN .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2001, 46 (09) :1477-1483

[7] A note on the existence, uniqueness and symmetry of par-balanced realizations [J].

Gheondea, A ;

Ober, RJ .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2000, 37 (04) :423-436

[8] ALL OPTIMAL HANKEL-NORM APPROXIMATIONS OF LINEAR-MULTIVARIABLE SYSTEMS AND THEIR L INFINITY-ERROR BOUNDS [J].

GLOVER, K .

INTERNATIONAL JOURNAL OF CONTROL, 1984, 39 (06) :1115-1193

[9] AN IMPROVED ERROR ESTIMATE FOR REDUCED-ORDER MODELS OF DISCRETE-TIME-SYSTEMS [J].

HINRICHSEN, D ;

PRITCHARD, AJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1990, 35 (03) :317-320

[10]

KATO T., 1966, Perturbation Theory for Linear Operators

← 1 2 3 →