The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials

Abstract This paper is devoted to prove the controllability to trajectories of a system of n one-dimensional parabolic equations when the control is exerted on a part of the boundary by means of m controls. We give a general Kalman condition (necessary and sufficient) and also present a construction and sharp estimates of a biorthogonal family in L 2 ( 0 , T ; C ) to { t j e − Λ k t } .

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