# Equivalent one-dimensional first-order linear hyperbolic systems and range of the minimal null control time with respect to the internal coupling matrix

Abstract : In this paper, we are interested in the minimal null control time of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls. Our main result is an explicit characterization of the smallest and largest values that this minimal null control time can take with respect to the internal coupling matrix. In particular, we obtain a complete description of the situations where the minimal null control time is invariant with respect to all the possible choices of internal coupling matrices. The proof relies on the notion of equivalent systems, in particular the backstepping method, a canonical $LU$-decomposition for boundary coupling matrices and a compactness-uniqueness method adapted to the null controllability property.
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https://hal.archives-ouvertes.fr/hal-03346287
Contributor : Guillaume Olive Connect in order to contact the contributor
Submitted on : Thursday, September 16, 2021 - 11:23:58 AM
Last modification on : Friday, September 17, 2021 - 3:07:24 AM

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• HAL Id : hal-03346287, version 1

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Long Hu, Guillaume Olive. Equivalent one-dimensional first-order linear hyperbolic systems and range of the minimal null control time with respect to the internal coupling matrix. 2021. ⟨hal-03346287⟩

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