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Summary  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 system states onto an orthogonal basis of Legendre polynomials. Numerical examples comparing these results with the ones in the literature are presented along with demonstrations of the effectiveness of the developed robust stability criteria.

Input/output stability of a damped string equation coupled with ordinary differential system