Well-posedness and controllability of a class of coupled linear systems

George Weiss*, Xiaowei Zhao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider coupled systems consisting of an infinite-dimensional part and a finite-dimensional part 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 infinite-dimensional part is assumed to be such that it becomes well-posed and strictly proper when connected in cascade with an integrator. 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 difference 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 coupled systems.

Original languageEnglish
Pages (from-to)2719-2750
Number of pages32
JournalSIAM Journal on Control and Optimization
Issue number4
StatePublished - 2009


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


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