Stabilization of Unstable Distributed Port-Hamiltonian Systems in Scattering Form

—In this letter, we consider the exponential
stabilization of a distributed parameter port-Hamiltonian
system interconnected with an unstable finite-dimensional
linear system at its free end and control input at the
opposite one. The infinite-dimensional system can also
have in-domain anti-damping. The control design passes
through the definition of a finite-dimensional linear system
that “embeds” the response of the distributed parameter
model, and that can be stabilized by acting on the available
control input. The conditions that link the exponential stability of the latter system with the exponential stability of
the original one are obtained thanks to a Lyapunov analysis. Simulations are presented to show the pros and cons
of the proposed synthesis methodology.