State Feedback Synthesis for Robust Performance with Probabilistic Parametric Uncertainty

The paper presents a convex-optimization-based approach to synthesize robust full-state feedback controllers in the presence of probabilistic parametric uncertainty. The known probability distribution of the uncertain parameters is used to determine probabilistic sector bounds on the uncertainty. The proposed synthesis method results in a controller that ensures robust stability with high probability, while maximizing closed-loop performance for the most likely values of uncertainty. The method involves iteratively solving semidefinite programs within a bisection or coordinate descent scheme. A numerical example demonstrates the performance improvement achieved by the proposed method in the presence of probabilisitic parametric uncertainty compared to a controller designed with the typical assumption of uniform uncertainty distributions.