Exact controllability of coupled PDE-ODE systems

George Weiss*, Xiaowei Zhao

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider coupled systems consisting of an infinite-dimensional part (a PDE system) and a finite-dimensional part (an ODE system) connected in feedback, such as for example the well-known SCOLE system (a beam with a rigid body attached at one end). The external world interacts with the coupled system via the finite-dimensional part, which receives the external input and sends out the output. The in finite-dimensional part is assumed to be a system node. Under several assumptions, we derive well-posedness and exact controllability results for such coupled systems. The first main result concerns the case when the input signal of the finite-dimensional part is the difierence between the external input and the feedback signal. The second main result allows a more general structure for the finite-dimensional part. We also prove a result for the approximate controllability of the coupled system.

Original languageEnglish
Title of host publicationROCOND'09 - 6th IFAC Symposium on Robust Control Design, Proceedings
Number of pages5
EditionPART 1
StatePublished - 2009
Event6th IFAC Symposium on Robust Control Design, ROCOND'09 - Haifa, Israel
Duration: 16 Jun 200918 Jun 2009

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670


Conference6th IFAC Symposium on Robust Control Design, ROCOND'09


  • Admissible control operator
  • Coupled system
  • Exact controllability
  • Simultaneous controllability
  • System node
  • Well-posed system


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