Study of the nodal feedback stabilization of a string-beams network

We consider a stabilization problem for a string-beams network. We prove an exponential decay result. The method used is based on a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent. Moreover, we give a numerical illustration based on the methodology introduced in Ammari and Tucsnak (ESAIM Control Optim. Calc. Var. 6, 361-386, 2001) where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined to a boundedness property of the transfer function of the associated open loop system. © 2010 Korean Society for Computational and Applied Mathematics.