Interpolatory H2-optimality Conditions for Structured Linear Time-invariant Systems
Abstract
Interpolatory necessary optimality conditions for H2-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on L2-optimal reduced-order modeling of stationary parametric problems, in this paper we develop and investigate optimality conditions for H2-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.
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