This chapter deals about the robust stability analysis of a coupled system made up of an uncertain ordinary differential system and a string equation. The main result states the robust exponential stability of this interconnected system subject to polytopic uncertainties. The Lyapunov theory transforms the stability analysis into the resolution of a set of linear matrix inequalities. They are obtained using projections of the infinite dimensional state onto the orthogonal basis of Legendre poly-nomials. The special structure of these inequalities is used to derive robust stability results. An example synthesizes the two main contributions of this chapter: an extended stability result and a robustness analysis. The example shows the efficiency of the proposed method.