On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems
Mehdi Badra, Takéo Takahashi (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper, we consider the well-known Fattorini’s criterion for approximate controllability of infinite dimensional linear systems of type ′ = + . We precise the result proved by Fattorini in [H.O. Fattorini, 4 (1966) 686–694.] for bounded input , in the case where can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini’s criterion is satisfied and if the set of geometric multiplicities of is bounded then approximate controllability...