An Orbit Robust Control Based on Linear Matrix Inequalities

This paper considers the problem of satellite's orbit control and a solution based in Linear Matrix Inequalities (LMI) is proposed for the case of Low Earth Orbiters (LEO). In particular, the modelling procedure and the algorithm for control law synthesis are tested using as study case the European Gravity Field and Ocean Circulation Explorer satellite (GOCE), to be launched by the European Space Agency (ESA) in the year 2006. The scientific objective of this space mission is the recovering of the Earth gravity field with high accuracy (less than 10${\mu}m$/${\mu}m$) and spatial resolution (better than 100km). In order to meet these scientific requirements, the orbit control must guarantee stringent specifications in terms of environmental disturbances attenuation (atmospheric drag forces) even in presence of high levels of model uncertainty.