Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE (Q2061008)

The main result of this paper is a methodology of global stabilization of a systems in cascade, in which the first subsystem is described by an ordinary differential equation (ODE) and the second is an infinite-dimensional one composed by a dissipative infinite-dimensional system and a system described by an ODE. The control appearing in the dynamics of the ODE, is subject to a general class of nonlinearities, namely cone-bounded nonlinearities. The feedback design is based on an extension of a finite-dimensional method, namely the forwarding method, which uses an infinite dimensional Sylvester equation. Based on appropriate observability assumption, it is proved that this design leads to a stabilizing feedback law. A necessary condition implying the above observability property is also provided. Some sufficient conditions that imply the well-posedness and the global asymptotic stability of the closed-loop system are also given. To illustrate the presented results, an application in a transport equation coupled with an ODE are finally considered.