Forwarding-Lyapunov design for the stabilization of coupled ODEs and exponentially stable PDEs

Swann Marx (1) , Daniele Astolfi (2) , Vincent Andrieu (2)

1 LS2N - Laboratoire des Sciences du Numérique de Nantes
2 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique

This paper is about the stabilization of a cascade system composed by an infinite-dimensional system, that we suppose to be exponentially stable, and an ordinary differential equation (ODE), that we suppose to be marginally stable. The system is controlled through the infinite-dimensional system. Such a structure is particularly useful when applying the internal model approach on infinite-dimensional systems. Our strategy relies on the forwarding method, which uses a Lyapunov functional and a Sylvester equation to build a feedback-law. Under some classical assumptions in the output regulation theory, we prove that the closed-loop system is globally exponentially stable.

Domaines: Automatique; Equations aux dérivées partielles [math.AP]

Swann Marx, Daniele Astolfi, Vincent Andrieu. Forwarding-Lyapunov design for the stabilization of coupled ODEs and exponentially stable PDEs. European Control Conference 2022, Jul 2022, Londres, United Kingdom. ⟨hal-03417238v1⟩