An extension of the argument principle and nyquist criterion to a class of systems with unbounded

Makan Fardad; Bassam Bamieh

doi:10.1109/TAC.2007.914233

An extension of the argument principle and nyquist criterion to a class of systems with unbounded

Makan Fardad, Bassam Bamieh

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The Nyquist stability criterion is generalized to systems where the open-loop system has infinite-dimensional input and output spaces and an unbounded infinitesimal generator. The infinitesimal generator is assumed to be a sectorial operator with trace-class resolvent. The main result is obtained through use of the perturbation determinant and an extension of the argument principle to infinitesimal generators with trace-class resolvents.

Original language	English (US)
Pages (from-to)	379-384
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	53
Issue number	1
DOIs	https://doi.org/10.1109/TAC.2007.914233
State	Published - Jan 2008
Externally published	Yes

Keywords

Argument principle
Infinite-dimensional system
Nyquist stability criterion
Perturbation determinant
Unbounded infinitesimal generator

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2007.914233

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abstract = "The Nyquist stability criterion is generalized to systems where the open-loop system has infinite-dimensional input and output spaces and an unbounded infinitesimal generator. The infinitesimal generator is assumed to be a sectorial operator with trace-class resolvent. The main result is obtained through use of the perturbation determinant and an extension of the argument principle to infinitesimal generators with trace-class resolvents.",

keywords = "Argument principle, Infinite-dimensional system, Nyquist stability criterion, Perturbation determinant, Unbounded infinitesimal generator",

author = "Makan Fardad and Bassam Bamieh",

note = "Funding Information: Manuscript received May 8, 2006; revised December 11, 2006 and June 28, 2007. Recommended by Associate Editor D. Dochain. This work was supported in part by the Air Force Office of Scientific Research under Grant FA9550-04-1-0207 and in part by the National Science Foundation under Grant ECS-0323814.",

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AU - Bamieh, Bassam

N1 - Funding Information: Manuscript received May 8, 2006; revised December 11, 2006 and June 28, 2007. Recommended by Associate Editor D. Dochain. This work was supported in part by the Air Force Office of Scientific Research under Grant FA9550-04-1-0207 and in part by the National Science Foundation under Grant ECS-0323814.

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N2 - The Nyquist stability criterion is generalized to systems where the open-loop system has infinite-dimensional input and output spaces and an unbounded infinitesimal generator. The infinitesimal generator is assumed to be a sectorial operator with trace-class resolvent. The main result is obtained through use of the perturbation determinant and an extension of the argument principle to infinitesimal generators with trace-class resolvents.

AB - The Nyquist stability criterion is generalized to systems where the open-loop system has infinite-dimensional input and output spaces and an unbounded infinitesimal generator. The infinitesimal generator is assumed to be a sectorial operator with trace-class resolvent. The main result is obtained through use of the perturbation determinant and an extension of the argument principle to infinitesimal generators with trace-class resolvents.

KW - Argument principle

KW - Infinite-dimensional system

KW - Nyquist stability criterion

KW - Perturbation determinant

KW - Unbounded infinitesimal generator

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An extension of the argument principle and nyquist criterion to a class of systems with unbounded

Abstract

Keywords

ASJC Scopus subject areas

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