  We propose a robust data-driven output feedback control algorithm that
explicitly incorporates inherent finite-sample model estimate uncertainties
into the control design. The algorithm has three components: (1) a subspace
identification nominal model estimator; (2) a bootstrap resampling method that
quantifies non-asymptotic variance of the nominal model estimate; and (3) a
non-conventional robust control design method comprising a coupled optimal
dynamic output feedback filter and controller with multiplicative noise. A key
advantage of the proposed approach is that the system identification and robust
control design procedures both use stochastic uncertainty representations, so
that the actual inherent statistical estimation uncertainty directly aligns
with the uncertainty the robust controller is being designed against. Moreover,
the control design method accommodates a highly structured uncertainty
representation that can capture uncertainty shape more effectively than
existing approaches. We show through numerical experiments that the proposed
robust data-driven output feedback controller can significantly outperform a
certainty equivalent controller on various measures of sample complexity and
stability robustness.
