Iterative $\mathcal{H}_{2}$ -Conic Controller Synthesis

The Conic Sector Theorem is a versatile input-output stability result that can be used to ensure closed-loop, input-output stability where better-known results, such as the Passivity and Small Gain Theorems, cannot. This paper proposes a linear-matrix-inequality-based approach to the synthesis of conic controllers that minimizes an upper bound on the closed-loop $mathcal{H}_{2}$ -norm. The upper bound is iteratively improved, providing controllers that successively decrease an upper bound on the closed-loop $mathcal{H}_{2}$ -norm. This provides a valuable tool for robust and optimal control by combining the utility of conic sectors and the Conic Sector Theorem with $mathcal{H}_{2}$ -optimal control. The effectiveness of this method is compared to an existing conic controller synthesis method in a numerical example.