Continuity properties of the real/complex structured singular value

Author

Packard, Andy ; Pandey, Pradeep

Author_Institution

Dept. of Mech. Eng., California Univ., Berkeley, CA, USA

Volume

38

Issue

3

fYear

1993

fDate

3/1/1993 12:00:00 AM

Firstpage

415

Lastpage

428

Abstract

The structured singular-value function (μ) is defined with respect to a given uncertainty set. This function is continuous if the uncertainties are allowed to be complex. However, if some uncertainties are required to be real, then it can be discontinuous. It is shown that μ is always upper semi-continuous, and conditions are derived under which it is also lower semi-continuous. With these results, the real-parameter robustness problem is reexamined. A related (although not equivalent) problem is formulated, which is always continuous, and the relationship between the new problem and the original real-μm problem is made explicit. A numerical example and results obtained via this related problem are presented

Keywords

matrix algebra; set theory; lower semi-continuous; matrix algebra; real-parameter robustness problem; real/complex structured singular value; set theory; uncertainty set; upper semi-continuous; Differential equations; Frequency; Linear algebra; Linear systems; Mechanical engineering; Performance analysis; Robust stability; Robustness; System testing; Uncertainty;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.210140

Filename

210140