Model Reduction for Fractional-Order Port-Hamiltonian Systems in the Loewner Framework

This paper addresses the problem of model order reduction for fractional-order port-Hamiltonian systems (FoPHS) within the Loewner framework. Building on the classical Loewner approach, the study extended the framework to incorporate fractional-order dynamics while preserving the port-Hamiltonian structure in reduced-order models. Specifically, the method was adapted to fractional-order systems by employing right- and left-tangential interpolation data, deriving conditions for constructing an interpolant that retains both the fractional-order behavior and the energy-conserving structure. Additionally, a novel interpolation data selection method was proposed, and numerical simulations validated the reduction approach, demonstrating its effectiveness and accuracy in preserving the system's inherent properties.