ℋ2 Control for Differential-Algebraic Systems

For a differential-algebraic system we construct an optimal ${\mathcal{H}_2}$ stabilizing controller and give a formula for the minimal ${\mathcal{H}_2}$ norm in terms of realizations and solutions to appropriate Riccati equations. Additionally, via the Youla parametrization, we construct a suboptimal controller that is guaranteed to be proper and which ensures an ${\mathcal{H}_2}$ norm that is arbitrarily close to the optimal one.