Coercive ISS-Lyapunov functionals for regular infinite-dimensional systems and applications

Abstract

This paper proposes the construction of a coercive ISS-Lyapunov functional for linear regular infinite-dimensional system. Indeed, as already known, Lyapunov functionals for infinite-dimensional systems might be not coercive. Under the assumption that there exists an exactly observable output, we are able to make coercive a Lyapunov functional which is not coercive under additional regularity assumption. We discuss also about 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, the Korteweg-de Vries equation.