<p>This paper proposes a procedure for constructing a coercive ISS-Lyapunov functional for regular infinite-dimensional systems that are exponentially stable. Indeed, as already known, Lyapunov functionals for infinite-dimensional systems do not need to be coercive. Under the assumption that there exists an exactly observable output, we are able to modify any non-coercive Lyapunov functional into a coercive one. We also discuss the potential applications of such a Lyapunov functional in singular perturbation theory and output regulation. The results are illustrated on a non-trivial equation, namely a linearized version of the Korteweg–de Vries equation.</p>