Gap metrics for time-varying linear systems in a continuous-time setting

Sei Zhen Khong; Michael Cantoni

doi:10.1016/j.sysconle.2014.06.003

Gap metrics for time-varying linear systems in a continuous-time setting

Sei Zhen Khong
, Michael Cantoni

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A recently proposed time-varying generalisation of Vinnicombe's ν-gap is shown to have the properties of a metric on a class of causal linear continuous-time systems that admit normalised strong graph representations. An alternative time-varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections. Finally, it is shown that the time-varying gap and ν-gap metrics induce the same topology, this being the coarsest topology under which feedback stability and closed-loop sensitivity are both robust properties.

Original language	English (US)
Pages (from-to)	118-126
Number of pages	9
Journal	Systems and Control Letters
Volume	70
DOIs	https://doi.org/10.1016/j.sysconle.2014.06.003
State	Published - Aug 2014
Externally published	Yes

Bibliographical note

Funding Information:
This work was supported by the Swedish Research Council through the LCCC Linnaeus centre and the Australian Research Council ( DP130104510 ). This paper was not presented at any IFAC meeting.

Keywords

Feedback
Linear time-varying systems
Robust stability

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10.1016/j.sysconle.2014.06.003

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title = "Gap metrics for time-varying linear systems in a continuous-time setting",

abstract = "A recently proposed time-varying generalisation of Vinnicombe's ν-gap is shown to have the properties of a metric on a class of causal linear continuous-time systems that admit normalised strong graph representations. An alternative time-varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections. Finally, it is shown that the time-varying gap and ν-gap metrics induce the same topology, this being the coarsest topology under which feedback stability and closed-loop sensitivity are both robust properties.",

keywords = "Feedback, Linear time-varying systems, Robust stability",

author = "Khong, \{Sei Zhen\} and Michael Cantoni",

note = "Funding Information: This work was supported by the Swedish Research Council through the LCCC Linnaeus centre and the Australian Research Council ( DP130104510 ). This paper was not presented at any IFAC meeting. ",

year = "2014",

month = aug,

doi = "10.1016/j.sysconle.2014.06.003",

language = "English (US)",

volume = "70",

pages = "118--126",

journal = "Systems and Control Letters",

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publisher = "Elsevier B.V.",

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T1 - Gap metrics for time-varying linear systems in a continuous-time setting

AU - Khong, Sei Zhen

AU - Cantoni, Michael

N1 - Funding Information: This work was supported by the Swedish Research Council through the LCCC Linnaeus centre and the Australian Research Council ( DP130104510 ). This paper was not presented at any IFAC meeting.

PY - 2014/8

Y1 - 2014/8

N2 - A recently proposed time-varying generalisation of Vinnicombe's ν-gap is shown to have the properties of a metric on a class of causal linear continuous-time systems that admit normalised strong graph representations. An alternative time-varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections. Finally, it is shown that the time-varying gap and ν-gap metrics induce the same topology, this being the coarsest topology under which feedback stability and closed-loop sensitivity are both robust properties.

AB - A recently proposed time-varying generalisation of Vinnicombe's ν-gap is shown to have the properties of a metric on a class of causal linear continuous-time systems that admit normalised strong graph representations. An alternative time-varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections. Finally, it is shown that the time-varying gap and ν-gap metrics induce the same topology, this being the coarsest topology under which feedback stability and closed-loop sensitivity are both robust properties.

KW - Feedback

KW - Linear time-varying systems

KW - Robust stability

UR - https://www.scopus.com/pages/publications/84903591431

UR - https://www.scopus.com/pages/publications/84903591431#tab=citedBy

U2 - 10.1016/j.sysconle.2014.06.003

DO - 10.1016/j.sysconle.2014.06.003

M3 - Article

AN - SCOPUS:84903591431

SN - 0167-6911

VL - 70

SP - 118

EP - 126

JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

Gap metrics for time-varying linear systems in a continuous-time setting

Abstract

Bibliographical note

Keywords

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