SIAM Journal on Control and Optimization, Vol.57, No.3, 1818-1844, 2019
WELL-POSEDNESS AND STABILITY OF INFINITE-DIMENSIONAL LINEAR PORT-HAMILTONIAN SYSTEMS WITH NONLINEAR BOUNDARY FEEDBACK
Boundary feedback stabilization of linear infinite dimensional port-Hamiltonian systems on an interval is considered. Generation and stability results already known for linear feedback are extended to nonlinear dissipative feedback, both to static feedback control and dynamic control via an (exponentially stabilizing) nonlinear controller. A design method for nonlinear controllers of linear port-Hamiltonian systems is introduced. As a special case the Euler-Bernoulli beam is considered.
Keywords:infinite-dimensional port-Hamiltonian systems;hybrid systems;nonlinear feedback;stabilization;nonlinear semigroups