H2 Output Feedback Control of Differential-Algebraic Systems

By employing the properties of centered realizations, we devise a modified version of the dual Riccati equation approach to optimal $\mathcal {H}_{2}$ control for differential-algebraic systems that is guaranteed to be more computationally efficient and numerically accurate than other methods from literature. Moreover, we show that if the optimal controller has an improper transfer function matrix, then all controllers which ensure a finite $\mathcal {H}_{2}$ norm will share this property.