Geodesic
Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 117.

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We show that under Kalman’s rank condition on the coupling matrices, the uniqueness of solution to a complex system of elliptic operators can be reduced to the observability of a scalar problem. Based on this result, we establish the asymptotic stability and the asymptotic synchronization for a large class of linear dissipative systems.

DOI : 10.1051/cocv/2020062
Classification : 93B05, 93C20, 35L53
Keywords: uniqueness, elliptic systems, asymptotic synchronization, condition of compatibility, Kalman’s rank condition 
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     author = {Li, Tatsien and Rao, Bopeng},
     editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinsk, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
     title = {Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
     doi = {10.1051/cocv/2020062},
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     zbl = {1461.93416},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2020062/}
}
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Li, Tatsien; Rao, Bopeng. Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 117. doi : 10.1051/cocv/2020062. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2020062/

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