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This paper deals with the stabilization of a coupled system composed by aninfinite-dimensional system and an ODE. Moreover, the control, which appears inthe dynamics of the ODE, is subject to a general class of nonlinearities. Sucha situation may arise, for instance, when the actuator admits a dynamics. Theopen-loop ODE is exponentially stable and the open-loop infinite-dimensionalsystem is dissipative, i.e., the energy is nonincreasing, but its equilibriumpoint is not necessarily attractive. The feedback design is based on anextension of a finite-dimensional method, namely the forwarding method. Wepropose some sufficient conditions that imply the well-posedness and the globalasymptotic stability of the closed-loop system. As illustration, we apply theseresults to a transport equation coupled with an ODE.

Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE