Normalized doubly coprime factorizations for infinite-dimensional linear systems

RF Curtain*, MR Opmeer

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)


We obtain explicit formulas for normalized doubly coprime factorizations of the transfer functions of the following class of linear systems: the input and output operators are vector-valued, but bounded, and the system is input and output stabilizable. Moreover, we give explicit formulas for the Bezout factors. Using a reciprocal approach, we extend our results to a larger class where the input and output operators are allowed to be unbounded. This class is much larger than the class of well-posed linear systems.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalMathematics of control signals and systems
Issue number1
Publication statusPublished - Feb-2006


  • infinite-dimensional linear systems
  • coprime factorizations
  • regular linear systems
  • stability
  • stabilizability
  • Riccati equations
  • Lyapunov equations
  • Bezout equations
  • Nehari problem
  • well-posed linear systems
  • operator nodes

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