We consider a tree-shaped network of vibrating strings. The problem of controllability when the control acts on the root of the tree is analyzed. We give a necessary and sufficient condition for the approximate controllability of the system in time 2(ℓ1++ℓM), where ℓ1,...,ℓMdenote the lengths of the strings of the network. This is a non-degeneracy condition guaranteeing that the spectra of any two subtrees of the network connected at a multiple node are mutually disjoint. © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.
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