Rank preservation of matrices with structured uncertainties and its applications in robust control theory

Author

Fong, I-Kong ; Tseng, Chwan-Lu ; Su, Juing-Huei

Author_Institution

Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan

Volume

40

Issue

8

fYear

1995

fDate

8/1/1995 12:00:00 AM

Firstpage

1461

Lastpage

1464

Abstract

Matrix rank is determined by the nonsingularity of its submatrices. For matrices in which entries are quadratic functions of some uncertain parameters, this paper derives sufficient conditions on parameters to that ensure the matrices preserve to some degrees the ranks they have when the parameters are all zero. The rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix in discussion, and suitable tools such as the μ-analysis method are used to solve the problem. Applications in robust control theory, including tests for robust controllability/observability, minimum phaseness, coprimeness, and Schur stability, are given, together with illustrative examples,

Keywords

control system analysis; matrix algebra; robust control; μ-analysis method; Schur stability; coprimeness; minimum phaseness; nonsingularity; nonsingularity analysis problem; quadratic functions; rank preservation; robust control theory; robust controllability/observability; structured uncertainties; submatrices; sufficient conditions; Controllability; Matrix converters; Observability; Robust control; Robust stability; Robustness; Sufficient conditions; Testing; Transfer functions; Uncertainty;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.402241

Filename

402241