Stability tests for one- two- and multidimensional linear systems

Author

Jury, E.I.

Author_Institution

University of California, Department of Electrical Engineering & Computer Sciences and Electronics Research Laboratory, Berkeley, USA

Volume

124

Issue

12

fYear

1977

fDate

12/1/1977 12:00:00 AM

Firstpage

1237

Lastpage

1240

Abstract

The paper reviews analytical stability tests for 1-dimensional linear systems since the early tests of E.J. Routh in his famous Adams Prize essay of 1877. The historical background of Routh´s stability test and criterion, as well as Fuller´s conjecture on its simplification, will be mentioned. In the historical review, the works of Hermite, Sylvester, Maxwell and others as related to the stability problem are also discussed. This review provides the context for a discussion of recent stability tests obtained for 2-dimensional and multidimensional linear systems. These tests are described and their computational complexity discussed in detail. In addition, the applications of stability testing to the study of 2- and multidimensional digital filters, numerical analysis of stiff-differential equations, realisation of mixed lumped- and distributed parameter systems, and the design of output feedback systems will be briefly mentioned. Comments on future research in this area conclude the review.

Keywords

large-scale systems; linear systems; stability; digital filters; distributed parameter systems; lumped parameter system; multidimensional linear systems; one dimensional linear system; output feedback systems; stability tests;

fLanguage

English

Journal_Title

Electrical Engineers, Proceedings of the Institution of

Publisher

iet

ISSN

0020-3270

Type

jour

DOI

10.1049/piee.1977.0260

Filename

5253429