  This paper deals with the problem of output regulation for systems defined on
matrix Lie-Groups. Reference trajectories to be tracked are supposed to be
generated by an exosystem, defined on the same Lie-Group of the controlled
system, and only partial relative error measurements are supposed to be
available. These measurements are assumed to be invariant and associated to a
group action on a homogeneous space of the state space. In the spirit of the
internal model principle the proposed control structure embeds a copy of the
exosystem kinematic. This control problem is motivated by many real
applications fields in aerospace, robotics, projective geometry, to name a few,
in which systems are defined on matrix Lie-groups and references in the
associated homogenous spaces.
