Abstract
The H2-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 H2norm. 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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