A note on a class of conservative, well-posed linear control systems

Rainer Picard, Sascha Trostorff, Marcus Waurick

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Citations (Scopus)

Abstract

We discuss a class of linear control problems in a Hilbert space setting. The aim is to show that these control problems fit in a particular class of evolutionary equations such that the discussion of well-posedness becomes easily accessible. Furthermore, we study the notion of conservativity. For this purpose we require additional regularity properties of the solution operator in order to allow point-wise evaluations of the solution. We exemplify our findings by a system with unbounded control and observation operators.
Original languageEnglish
Title of host publication Progress in Partial Differential Equations
Subtitle of host publicationAsymptotic Profiles, Regularity and Well-Posedness
Place of PublicationHeidelberg
PublisherSpringer
Pages261-286
Number of pages26
ISBN (Print)9783319001241
DOIs
Publication statusPublished - 29 May 2013

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume44
ISSN (Print)2194-1009

Keywords

  • Hilbert space
  • linear control systems
  • evolutionary equations
  • conservativity
  • well-posedness

Cite this

Picard, R., Trostorff, S., & Waurick, M. (2013). A note on a class of conservative, well-posed linear control systems. In Progress in Partial Differential Equations: Asymptotic Profiles, Regularity and Well-Posedness (pp. 261-286). (Springer Proceedings in Mathematics & Statistics; Vol. 44). Springer. https://doi.org/10.1007/978-3-319-00125-8