On the metric property of an LTV generalisation of the ν-gap

Author

Sei Zhen Khong ; Cantoni, Marco

Author_Institution

Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia

fYear

2012

fDate

10-13 Dec. 2012

Firstpage

214

Lastpage

219

Abstract

A recent linear time-varying (LTV) generalisation of Vinnicombe´s ν-gap metric is defined in terms of normalised strong representations of system graphs and a Fredholm index constraint on a family of Toeplitz-Wiener-Hopf operators, parameterised by start time. It is shown in this paper that the LTV definition is invariant with respect to the choice of graph representations and that it is indeed a metric. For a class of time-invariant systems, the generalised ν-gap reduces to the original frequency-domain definition.

Keywords

graph theory; linear systems; time-varying systems; Fredholm index constraint; LTV generalisation; Toeplitz-Wiener-Hopf operators; Vinnicombe ν-gap metric; frequency-domain definition; linear time-varying generalisation; normalised strong graph representations; start time; time-invariant systems; Abstracts; Hilbert space; Indexes; Robustness; Stability analysis; Time varying systems; ν-gap metric; linear time-varying systems; strong graph representations;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2012 IEEE 51st Annual Conference on

Conference_Location

Maui, HI

ISSN

0743-1546

Print_ISBN

978-1-4673-2065-8

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2012.6427107

Filename

6427107