  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.
