Linear feedback spacecraft stabilization using the method of invariant ellipsoids

This paper addresses the robust attitude control for an uncertain flexible spacecraft with disturbances bounded by ellipsoids. An observed-state feedback is designed using the so-called invariant ellipsoid method, which is based on the local invariant set theorem. The minimum invariant ellipsoid can be considered as the influence of the uncertainties and disturbances in the controlled system. All these considerations were expressed through LMI technique as an optimization problem with linear objective and LMI constraints. The numerical solution of this problem gives the parameters for the linear controller and the Luenberger observer that guarantee a quasi-minimal invariant ellipsoid for the controlled spacecraft.