In this paper, we show that the independence of approximately synchronizable state $u$ by $p$-groups with respect to applied controls, the linear independence of the components, the non extensibility of the approximate synchronization by $p$-groups as well as the necessity of the condition of $C_p$-compatibility, all these properties are the consequence of the minimality of Kalman’s rank condition and vice versa. These results reveal the role of Kalman rank conditions on control problems from different aspects, and further develop the synchronization theory.
Dans cette note, nous montrons que l’indépendance de l’état de synchronisation approchée par rapport aux contrôles, la non extensibilité de la synchronisation approchée, l’indépendance linéaire des composants de l’état de synchronisation approchée ainsi que la condition de $C_p$-compatibilité, toutes ces propriétés sont la conséquence de la minimalité de la condition du rang de Kalman.
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Keywords: Kalman’s rank condition, approximate synchronization by groups, system of wave equations
Mots-clés : Condition du rang de Kalman, synchronisation approchée par groupes, système d’équations d’ondes
Tatsien Li 1 ; Bopeng Rao 2
CC-BY 4.0
@article{CRMATH_2025__363_G9_893_0,
author = {Tatsien Li and Bopeng Rao},
title = {Some fundamental properties of the approximate synchronization by groups for a coupled system of wave equations with internal controls},
journal = {Comptes Rendus. Math\'ematique},
pages = {893--904},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {363},
doi = {10.5802/crmath.642},
language = {en},
}
TY - JOUR AU - Tatsien Li AU - Bopeng Rao TI - Some fundamental properties of the approximate synchronization by groups for a coupled system of wave equations with internal controls JO - Comptes Rendus. Mathématique PY - 2025 SP - 893 EP - 904 VL - 363 PB - Académie des sciences, Paris DO - 10.5802/crmath.642 LA - en ID - CRMATH_2025__363_G9_893_0 ER -
%0 Journal Article %A Tatsien Li %A Bopeng Rao %T Some fundamental properties of the approximate synchronization by groups for a coupled system of wave equations with internal controls %J Comptes Rendus. Mathématique %D 2025 %P 893-904 %V 363 %I Académie des sciences, Paris %R 10.5802/crmath.642 %G en %F CRMATH_2025__363_G9_893_0
Tatsien Li; Bopeng Rao. Some fundamental properties of the approximate synchronization by groups for a coupled system of wave equations with internal controls. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 893-904. doi: 10.5802/crmath.642
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