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.
展开▼
机译：我们考虑了弦梁网络的稳定问题。我们证明了指数衰减的结果。所使用的方法基于频域方法，并将矛盾的论点与乘数技术相结合，以对分解体进行特殊分析。此外，我们根据Ammari和Tucsnak（ESAIM Control Optim。Calc。Var。6，361–386，2001）中介绍的方法给出了一个数值说明，其中，闭环问题的指数稳定性降低为可观察性估计值。相应的不受控制的系统，与相关的开环系统的传递函数的有界性相结合。
展开▼
