  Control of linear dynamics with multiplicative noise naturally introduces
robustness against dynamical uncertainty. Moreover, many physical systems are
subject to multiplicative disturbances. In this work we show how these dynamics
can be identified from state trajectories. The least-squares scheme enables
exploitation of prior information and comes with practical data-driven
confidence bounds and sample complexity guarantees. We complement this scheme
with an associated control synthesis procedure for LQR which robustifies
against distributional uncertainty, guaranteeing stability with high
probability and converging to the true optimum at a rate inversely proportional
with the sample count. Throughout we exploit the underlying multi-linear
problem structure through tensor algebra and completely positive operators. The
scheme is validated through numerical experiments.
