Shift-invariant representation of two periodic system classes defined over doubly-infinite continuous time

Sei Zhen Khong, Michael Cantoni

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

2 Scopus citations


This paper considers an isomorphism introduced by Bamieh et. al. in [1], to construct shift-invariant representations, over the same'time-lifted' system class, for two classes of linear periodically time-varying (LPTV) systems. Specifically, we consider the class of finite-dimensional linear time-invariant (LTI) systems, characterised by a rational frequency-domain symbol, and a class of LPTV systems with sampled-data structure. Such systems appear together in problems of sampled-data approximation, for example. We study them here in terms of mappings between finite-energy signals defined over the doubly-infinite continuous-time axis (-∞,∞), which arises when working with the ν-gap metric to gauge approximation error for such problems. A complication within this context stems from the absence of an integral-operator input-output representation for every system in the LPTV classes considered. We resolve this issue by working with the graph representation of the systems involved.

Original languageEnglish (US)
Title of host publicationProceedings of SICE Annual Conference 2010, SICE 2010 - Final Program and Papers
PublisherSociety of Instrument and Control Engineers (SICE)
Number of pages8
ISBN (Print)9784907764364
StatePublished - Jan 1 2010

Publication series

NameProceedings of the SICE Annual Conference


  • Doubly-infinite time
  • Multiplication operators
  • Periodic systems
  • Sampled-data systems


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