  This is a complementary document to the paper presented in [1], to provide
more detailed proofs for some results. The main paper addresses the problem of
trajectory tracking control of autonomous rotorcraft in operation scenarios
where only relative position measurements obtained from LiDAR sensors are
possible. The proposed approach defines an alternative kinematic model,
directly based on LiDAR measurements, and uses a trajectory-dependent error
space to express the dynamic model of the vehicle. An LPV representation with
piecewise affine dependence on the parameters is adopted to describe the error
dynamics over a set of predefined operating regions, and a continuous-time
$H_2$ control problem is solved using LMIs and implemented within the scope of
gain-scheduling control theory.
