H2 Model Reduction¶
Given model \(H\in \mathcal{H}_2\), the goal of model reduction is to find a simplified model \(H_r\in \mathcal{H}_2\) that minimizes the mismatch in the \(\mathcal{H}_2\) norm:
\[\min_{H_r} \| H - H_r\|_{\mathcal{H}_2}
\quad
\langle F, G \rangle_{\mathcal{H}_2} :=
\frac{1}{2\pi} \int_{-\infty}^\infty \overline{F(i\omega)} G(i\omega) \mathrm{d} \omega.\]