The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials |
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| Authors: | F. Ammar-Khodja,A. Benabdallah,M. Gonzá lez-Burgos,L. de Teresa |
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| Affiliation: | aLaboratoire de Mathématiques, Université de Franche-Comté, 16 route de Gray, 25030 Besancon Cedex, France;bCentre de Mathématiques et Informatique, Université Aix-Marseille 1, Technopôle Château-Gombert, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France;cDpto. E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain;dInstituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U. 04510 D.F., México, Mexico |
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| 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 L2(0,T;C) to {tje−Λkt}. |
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| Keywords: | Parabolic systems Boundary controllability Biorthogonal families Kalman rank condition |
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