Stabilization of a class of mixed ODE–PDE port-Hamiltonian systems with strong dissipation feedback

This paper deals with the asymptotic stabilization of a class port-Hamiltonian (pH) 1-D Partial Differential Equations (PDE) spatial varying parameters, interconnected linear Ordinary (ODE), control input on ODE. The considered ODE contains effect proportional term, that can be as action controller or spring in case mechanical systems. In this particular study, it is not possible to directly add damping boundary PDE. To remedy problem we propose law makes use “strong feedback” term. We first prove closed-loop operator generates contraction strongly continuous semigroup, then address stability making Lyapunov argument, taking advantage pH structure original system controlled. Furthermore, apply proposed for vibrating string tip mass and show simulation results compared application simple PD controller.