Stabilization of port-Hamiltonian systems by nonlinear boundary control in the presence of disturbances

In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems arbitrary order N ∈ ℕ on a bounded 1-dimensional spatial domain ( , b ). to achieve stabilization, couple system dynamic boundary controller, that is, controller acts only via points domain. We use nonlinear in capture behavior realistic actuators often exhibit and, moreover, allow output be corrupted by actuator disturbances before it is fed back into system. What show here resulting closed-loop input-to-state stable w.r.t. square-integrable disturbance inputs. particular, obtain uniform stability for = 1 and special class controllers, weak more general controllers. Also, both cases, convergence 0 all solutions as t → ∞ . Applications given vibrating strings beams.