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A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems

Abstract : In this paper we present a generalization of the Kalman rank condition for linear ordinary differential systems to the case of a systems of n coupled parabolic equations (posed in the time interval (0, T) with T > 0) where the coupling matrices A and B depend on the time variable t. To be precise, we will prove that the Kalman rank condition rank [A|B](t0) = n, with t0 in [0, T], is a sufficient condition (but not necessary) for obtaining the exact controllability to the trajectories of the considered parabolic system
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https://hal.archives-ouvertes.fr/hal-00472533
Contributor : Cédric Dupaix Connect in order to contact the contributor
Submitted on : Monday, April 12, 2010 - 2:02:02 PM
Last modification on : Thursday, January 13, 2022 - 12:00:02 PM

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  • HAL Id : hal-00472533, version 1

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Cédric Dupaix, F. Ammar Khodja, A. Benabdalah, M. Gonzalez-Burgos. A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems. Diff. Equ. and Appl., 2009, 1 (3), pp.427-457. ⟨hal-00472533⟩

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