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

Swann Marx

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arXiv · 2403.11596

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

Swann Marx

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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.

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Swann Marx. 2024-03-18. Coercive ISS-Lyapunov functionals for regular infinite-dimensional systems and applications. https://arxiv.org/abs/2403.11596

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