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

作者：Ammar Khodja F; Benabdallah A^*; Gonzalez Burgos M; de Teresa L

来源：Journal de Mathematiques Pures et Appliquees, 2011, 96(6): 555-590.

DOI：10.1016/j.matpur.2011.06.005

• Parabolic systems
• Boundary controllability
• Biorthogonal families
• Kalman rank condition

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 I{t(j)e(-Akt)}.

• 出版日期2011-12