EXPONENTIAL STABILISATION OF A TREE-SHAPED NETWORK OF STRINGS WITH VARIABLE COEFFICIENTS*

GUO, YAN NI ; XU, GEN QI

Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 481-499

Résumé

In this paper, we deal with a tree-shaped network of strings with a fixed root node. By imposing velocity feedback controllers on all vertices except the root node, we show that the spectrum of the system operator consists of all isolated eigenvalues of finite multiplicity and is distributed in a strip parallel to the imaginary axis under certain conditions. Moreover, we prove that there exists a sequence of eigenvectors and generalised eigenvectors that forms a Riesz basis with parentheses, and that the imaginary axis is not an asymptote of the spectrum. Thereby, we deduce that the system is exponentially stable.

Détail

DOI : 10.1017/S0017089511000085

Mots-clés : 93C20, 93D15, 35B35, 35P10, 47A70

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