We show that under Kalman’s rank condition, the observability of a scalar equation implies the uniqueness of solution to a system of elliptic operators. Using this result, we establish the asymptotic synchronization by groups for second order evolution systems.
Nous montrons que sous la condition du rang de Kalman, l’observabilité d’une équation scalaire implique l’unicité de la solution d’un système d’opérateurs elliptiques. En utilisant ce résultat, nous établissons la synchronisation asymptotique par groupes de systèmes d’évolution du second ordre.
Accepted:
Published online:
Tatsien Li 1; Bopeng Rao 2, 3, 4
@article{CRMATH_2020__358_3_285_0, author = {Tatsien Li and Bopeng Rao}, title = {Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization}, journal = {Comptes Rendus. Math\'ematique}, pages = {285--295}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {3}, year = {2020}, doi = {10.5802/crmath.31}, language = {en}, }
TY - JOUR AU - Tatsien Li AU - Bopeng Rao TI - Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization JO - Comptes Rendus. Mathématique PY - 2020 SP - 285 EP - 295 VL - 358 IS - 3 PB - Académie des sciences, Paris DO - 10.5802/crmath.31 LA - en ID - CRMATH_2020__358_3_285_0 ER -
%0 Journal Article %A Tatsien Li %A Bopeng Rao %T Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization %J Comptes Rendus. Mathématique %D 2020 %P 285-295 %V 358 %N 3 %I Académie des sciences, Paris %R 10.5802/crmath.31 %G en %F CRMATH_2020__358_3_285_0
Tatsien Li; Bopeng Rao. Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization. Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 285-295. doi : 10.5802/crmath.31. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.31/
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