Interpolation-based ℌ2 model reduction for port-Hamiltonian systems

Port network modeling of physical systems leads directly to an important class of passive state space systems: port-Hamiltonian systems. We consider here methods for model reduction of large scale port-Hamiltonian systems that preserve port-Hamiltonian structure and are capable of yielding reduced order models that satisfy first-order optimality conditions with respect to an H₂ system error metric. The methods we consider are closely related to rational Krylov methods and variants are described using both energy and co-energy system coordinates. The resulting reduced models have port-Hamiltonian structure and therefore are guaranteed passive, while still retaining the flexibility to interpolate the true system transfer function at any (complex) frequency points that are desired.