%0 Journal Article %T Input / Output Stability of a Damped String Equation coupled with Ordinary Differential System %+ Équipe Méthodes et Algorithmes en Commande (LAAS-MAC) %+ Northeastern University [Boston] %A Barreau, Matthieu %A Gouaisbaut, Frédéric %A Seuret, Alexandre %A Sipahi, Rifat %< avec comité de lecture %Z Rapport LAAS n° 18018 %@ 1049-8923 %J International Journal of Robust and Nonlinear Control %I Wiley %V 28 %N 18 %P 6053-6069 %8 2018-09-19 %D 2018 %Z 1801.09916 %R 10.1002/rnc.4357 %K Coupled ODE/PDE %K Robust stability %K String equation %K Frequency approach %K Quadratic Separation %Z Mathematics [math]/Optimization and Control [math.OC] %Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles %X The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived using pole locations. Then, based on the Small-Gain theorem and on the Quadratic Separation framework, some robust stability criteria are provided. The latter follows from a projection of the infinite dimensional state on an orthogonal basis of Legendre polynomials. Numerical examples comparing these results with the ones in the literature are proposed and a comparison of its efficiency is made. %G English %2 https://laas.hal.science/hal-01690626v2/document %2 https://laas.hal.science/hal-01690626v2/file/2018_Dirichlet_CTCR.pdf %L hal-01690626 %U https://laas.hal.science/hal-01690626 %~ UNIV-TLSE2 %~ UNIV-TLSE3 %~ CNRS %~ INSA-TOULOUSE %~ LAAS %~ INSMI %~ LAAS-MAC %~ UT1-CAPITOLE %~ LAAS-DECISION-ET-OPTIMISATION %~ TDS-MACS %~ INSA-GROUPE %~ ANR %~ TOULOUSE-INP %~ UNIV-UT3 %~ UT3-INP %~ UT3-TOULOUSEINP