A Kalman rank condition for the indirect controllability of coupled systems of linear operator groups

Original Article


In this article, we give a necessary and sufficient condition of Kalman type for the indirect controllability of systems of groups of linear operators, under some “regularity and locality” conditions on the control operator that will be made precise later and fit very well the case of distributed controls. Moreover, in the case of first order in time systems, when the Kalman rank condition is not satisfied, we characterize exactly the initial conditions that can be controlled. Some applications to the control of systems of Schrödinger or wave equations are provided. The main tool used here is the fictitious control method coupled with the proof of an algebraic solvability property for some related underdetermined system and some regularity results.


Controllability of abstract linear semi-groups Indirect controllability of systems Schrödinger and wave equations Fictitious control method Algebraic solvability 

Mathematics Subject Classification

35F35 35G35 47D03 93B05 93B07 


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Copyright information

© Springer-Verlag London 2017

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, CNRS UMR 7598Université Pierre et Marie Curie (Univ. Paris 6)ParisFrance
  2. 2.CEREMADEUniversité Paris-Dauphine & CNRS UMR 7534, PSL Research UniversityParisFrance

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