Regular implementation in the space of compactly supported functions

D. Napp Avelli, Shiva Shankar, H.L. Trentelman

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This article extends results on regular implementability in [P. Rocha, Canonical controllers and regular implementation of nd behaviors, in: Proceedings of the 16th IFAC World Congress, 20051 and [H.L. Trentelman, D. Napp Avelli, On the regular implementability of nD systems, Systems Control Lett. 56 (4) (2007) 265-271] to the case when the signal space is not an injective cogenerator, for instance, the space D of compactly supported smooth functions on R-n. In this case the bijective correspondence between behaviors and modules fails to hold; also projections and sums of behaviors need not in general be behaviors. A more general version of implementability is introduced and necessary and sufficient conditions are established for the implementation and regular implementation of a given desired behavior. (c) 2008 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)851-855
Number of pages5
JournalSystems & Control Letters
Issue number10
Publication statusPublished - Oct-2008


  • multidimensional behaviors
  • partial interconnection
  • implementability
  • Willems closure
  • injective cogenerators

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