Control of a satellite system with an electrodynamic tether as actuator is a time-periodic and underactuated control problem. This paper considers the tethered satellite in a Hamiltonian framework and determines a port-controlled Hamiltonian formulation that adequately describes the nonlinear dynamical system. Based on this model, a nonlinear controller id designed that will make the system asymptotically stable around its open-loop equilibrium. The control scheme handles the time-varying nature of the system in a suitable manner resulting in a large operational region. The performance of the closed loop system is treated using Floquet theory, investigating the closed loop properties for their dependency of the controller gain and orbit inclination.