  Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal
reduced-order modeling of unstructured linear time-invariant (LTI) systems are
well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order
modeling of stationary parametric problems, in this paper we develop and
investigate optimality conditions for $\mathcal{H}_2$-optimal reduced-order
modeling of structured LTI systems, in particular, for second-order,
port-Hamiltonian, and time-delay systems. Under certain diagonalizability
assumptions, we show that across all these different structured settings,
bitangential Hermite interpolation is the common form for optimality, thus
proving a unifying optimality framework for structured reduced-order modeling.
