The H 2 -optimal static output feedback control design for linear time-invariant systems with time-invariant probabilistic parametric uncertainties subject to disturbances and noise is formulated in terms of an optimization with a highly sparse bilinear matrix inequality (BMI) constraint. The BMI formulation is derived by employing polynomial chaos expansions to represent the effect of the parametric uncertainties on the H 2 norm. The effect of using a finite number of terms in the expansions is discussed and addressed by incorporating a robustifying parameter in the BMI formulation. In a case study, the feedback controller converges using a sixth-order expansion, with a substantial improvement in robustness to parametric uncertainty.
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