Finite dimensional approximations of unstable infinite dimensional systems

G. Gu; P. P. Khargonekar; E. B. Lee; P. Misra

doi:10.1109/cdc.1990.203787

Finite dimensional approximations of unstable infinite dimensional systems

G. Gu, P. P. Khargonekar, E. B. Lee, P. Misra

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The approximation of possibly unstable linear infinite-dimensional systems is studied. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. Under a certain mild frequency domain condition, a procedure is developed for constructing a sequence of finite-dimensional approximants which converges to the true model in the L∞ norm. It is noted that the proposed technique uses only the FFT (fast Fourier transform) and the singular value decomposition algorithms for obtaining the approximations. Some examples are included to illustrate the proposed method.

Original language	English
Title of host publication	29th IEEE Conference on Decision and Control
Publisher	IEEE
Pages	1168-1173
Number of pages	6
Volume	3
DOIs	https://doi.org/10.1109/cdc.1990.203787
State	Published - 1990
Event	29th IEEE Conference on Decision and Control - Honolulu, United States Duration: Dec 5 1990 → Dec 7 1990 Conference number: 29

Conference

Conference	29th IEEE Conference on Decision and Control
Country/Territory	United States
City	Honolulu
Period	12/5/90 → 12/7/90

ASJC Scopus Subject Areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Keywords

Transfer functions
Frequency domain analysis
Singular value decomposition
Contracts
Time domain analysis
Linear approximation
H infinity control
Control design
Approximation methods
Robustness

Disciplines

Applied Mathematics
Controls and Control Theory

Access to Document

10.1109/cdc.1990.203787

Cite this

@inproceedings{7d8c7834abd14df1b8553294312de0ac,

title = "Finite dimensional approximations of unstable infinite dimensional systems",

abstract = "The approximation of possibly unstable linear infinite-dimensional systems is studied. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. Under a certain mild frequency domain condition, a procedure is developed for constructing a sequence of finite-dimensional approximants which converges to the true model in the L∞ norm. It is noted that the proposed technique uses only the FFT (fast Fourier transform) and the singular value decomposition algorithms for obtaining the approximations. Some examples are included to illustrate the proposed method.",

keywords = "Transfer functions, Frequency domain analysis, Singular value decomposition, Contracts, Time domain analysis, Linear approximation, H infinity control, Control design, Approximation methods, Robustness",

author = "G. Gu and Khargonekar, {P. P.} and Lee, {E. B.} and P. Misra",

year = "1990",

doi = "10.1109/cdc.1990.203787",

language = "English",

volume = "3",

pages = "1168--1173",

booktitle = "29th IEEE Conference on Decision and Control",

publisher = "IEEE",

note = "29th IEEE Conference on Decision and Control ; Conference date: 05-12-1990 Through 07-12-1990",

}

TY - GEN

T1 - Finite dimensional approximations of unstable infinite dimensional systems

AU - Gu, G.

AU - Khargonekar, P. P.

AU - Lee, E. B.

AU - Misra, P.

N1 - Conference code: 29

PY - 1990

Y1 - 1990

N2 - The approximation of possibly unstable linear infinite-dimensional systems is studied. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. Under a certain mild frequency domain condition, a procedure is developed for constructing a sequence of finite-dimensional approximants which converges to the true model in the L∞ norm. It is noted that the proposed technique uses only the FFT (fast Fourier transform) and the singular value decomposition algorithms for obtaining the approximations. Some examples are included to illustrate the proposed method.

AB - The approximation of possibly unstable linear infinite-dimensional systems is studied. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. Under a certain mild frequency domain condition, a procedure is developed for constructing a sequence of finite-dimensional approximants which converges to the true model in the L∞ norm. It is noted that the proposed technique uses only the FFT (fast Fourier transform) and the singular value decomposition algorithms for obtaining the approximations. Some examples are included to illustrate the proposed method.

KW - Transfer functions

KW - Frequency domain analysis

KW - Singular value decomposition

KW - Contracts

KW - Time domain analysis

KW - Linear approximation

KW - H infinity control

KW - Control design

KW - Approximation methods

KW - Robustness

UR - http://www.scopus.com/inward/record.url?scp=0025550828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025550828&partnerID=8YFLogxK

U2 - 10.1109/cdc.1990.203787

DO - 10.1109/cdc.1990.203787

M3 - Conference contribution

AN - SCOPUS:0025550828

VL - 3

SP - 1168

EP - 1173

BT - 29th IEEE Conference on Decision and Control

PB - IEEE

T2 - 29th IEEE Conference on Decision and Control

Y2 - 5 December 1990 through 7 December 1990

ER -

Finite dimensional approximations of unstable infinite dimensional systems

Abstract

Conference

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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