Robust stability properties of the v-gap metric for time-varying systems

Sei Zhen Khong, Michael Cantoni, Ulf T. Jönsson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

The stability of uncertain feedback interconnections of causal time-varying linear systems is studied in terms of a recently established generalisation of the v-gap metric. In particular, a number of robustness results from the well-known linear time-invariant theory are extended. The time-varying generalisations include: sufficient conditions for robust stability; a bound on robust performance; and two-sided bounds on the induced norm of the variation in a closed-loop mapping as an open-loop component of the feedback interconnection is perturbed. Underlying assumptions are verified for causal systems that exhibit linear periodically time-varying behaviour. This includes a class of sampled-data systems as a special case. Within the periodic context considered, it can be shown that a robust stability condition is also necessary.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages2028-2033
Number of pages6
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

Keywords

  • Feedback
  • periodic systems
  • robust stability
  • time-varying systems
  • v-gap metric

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