  This paper deals with the stabilization of a coupled system composed by an
infinite-dimensional system and an ODE. Moreover, the control, which appears in
the dynamics of the ODE, is subject to a general class of nonlinearities. Such
a situation may arise, for instance, when the actuator admits a dynamics. The
open-loop ODE is exponentially stable and the open-loop infinite-dimensional
system is dissipative, i.e., the energy is nonincreasing, but its equilibrium
point is not necessarily attractive. The feedback design is based on an
extension of a finite-dimensional method, namely the forwarding method. We
propose some sufficient conditions that imply the well-posedness and the global
asymptotic stability of the closed-loop system. As illustration, we apply these
results to a transport equation coupled with an ODE.
