The aim of this paper is to consider the modelling and control issues arising in the design of a station keeping system for geostationary satellites based on electric propulsion. In particular, a linear time-varying model for the dynamics of a geostationary satellite affected by perturbations is derived and the longitude and latitude station keeping problem is then formulated as a constrained linear quadratic optimal control problem. A direct method based on the so-called differential inclusion

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... approach is then proposed. Simulation results showing the feasibility of the control task on a spacecraft equipped with electric thrusters are also presented and discussed.