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

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• 作者：F.  ; Ammar-Khodja^a ;   ; ¹ ;   ; ^{fammarkh@univ-fcomte.fr} ; A.  ; Benabdallah^b ;   ; ¹ ;   ; ^{assia@cmi.univ-mrs.fr} ; M.  ; Gonzá ; lez-Burgos^c ;   ; ² ;   ; ^{manoloburgos@us.es} ; L.  ; de Teresa^d ;   ; ³ ;   ; ^{deteresa@matem.unam.mx}
• 关键词：Parabolic systems ; Boundary controllability ; Biorthogonal families ; Kalman rank condition
• 刊名：Journal des Mathematiques Pures et Appliquees
• 出版年：2011
• 出版时间：December 2011
• 年：2011
• 卷：96
• 期：6
• 页码：555-590
• 全文大小：349 K

文摘

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 to .