Structured singular values with nondiagonal structures. I. Characterizations

Author

Chen, Jie ; Fan, Michael K H ; Nett, Carl N.

Author_Institution

Coll. of Eng., California Univ., Riverside, CA, USA

Volume

41

Issue

10

fYear

1996

fDate

10/1/1996 12:00:00 AM

Firstpage

1507

Lastpage

1511

Abstract

The purpose of this two-part series is to provide a robustness analysis framework for a class of problems with highly structured modeling uncertainties. This framework is more general than that of the usual block, diagonally structured uncertainties, and it corresponds to a structure consisting of block-by-block matrix perturbations. We study the structured singular value with respect to this structure, and we establish a number of novel results for this notion. This paper contains a study on the properties of the structured singular value. We give an alternative characterization of this notion as the solution of a smooth optimization problem. Furthermore, we show that under a certain circumstance the structured singular value reduces to a vector-induced matrix norm

Keywords

optimisation; perturbation techniques; singular value decomposition; stability; uncertain systems; matrix perturbations; nondiagonal structures; optimization; robustness analysis; structured modeling uncertainties; structured singular values; vector-induced matrix norm; Computational complexity; Feedback; Measurement standards; Robust stability; Robustness; Space technology; Stability analysis; Transfer functions; Uncertainty; Upper bound;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.539434

Filename

539434