An Extension of the Argument Principle and Nyquist Criterion to a Class of Systems With Unbounded Generators

Author

Fardad, Makan ; Bamieh, Bassam

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN

Volume

53

Issue

1

fYear

2008

Firstpage

379

Lastpage

384

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

Nyquist criterion; Nyquist stability; multidimensional systems; open loop systems; perturbation techniques; Nyquist stability criterion; argument principle; infinite-dimensional input-output system; open-loop system; perturbation determinant; trace-class resolvent; unbounded infinitesimal generator; Algebra; Eigenvalues and eigenfunctions; Equations; Feedback; Matrices; Performance analysis; Stability analysis; Stability criteria; System testing; Transfer functions; Argument principle; Nyquist stability criterion; infinite-dimensional system; perturbation determinant; unbounded infinitesimal generator;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2007.914233

Filename

4459796