  This paper addresses the lack of a general methodology for the controller
synthesis of an optical instrument on-board a stratospheric balloon-borne
platform, such as a telescope or siderostat, to meet pointing requirements that
are becoming more and more stringent in the context of astronomy missions. Most
often in the literature, a simple control structure is chosen, and the control
gains are tuned empirically based on ground testings. However, due to the large
dimensions of the balloon and the flight chain, experimental set-ups only
involve the pointing system and the platform, whereas flight experience shows
that the pointing performance is essentially limited by the rejection of the
natural pendulum-like oscillations of the fully deployed system. This
observation justifies the need for a model that predicts such flight conditions
that cannot be replicated in laboratory, and for an adequate methodology
addressing the line-of-sight controller design. In particular, it is necessary
to ensure robust stability and performance to the parametric uncertainties
inherent to balloon-borne systems, such as complex balloon's properties or
release of ballast throughout the flight, especially since experimental
validation is limited. In this paper, a dynamical model of the complete system
is proposed, based on a multibody approach and accounting for parametric
uncertainties with Linear Fractional Transformations. The comparison with
flight data shows that the frequency content of the platform's motion is
accurately predicted. Then, the robust control of the line-of-sight is tackled
as a $\mathcal H_{\infty}$ problem that allows to reach the performance
objectives in terms of disturbance rejection, control bandwidth and actuators
limitations.
