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In this paper we propose a solution to the problem of moment matching withpreservation of the port Hamiltonian structure, in the framework of time-domainmoment matching. We characterize several families of parameterized portHamiltonian models that match the moments of a given port Hamiltonian system,at a set of finite interpolation points. We also discuss the problem of Markovparameters matching for linear systems as a moment matching problem fordescriptor representations associated to the given system, at zerointerpolation points. Solving this problem yields families of parameterizedreduced order models that achieve Markov parameter matching. Finally, we applythese results to the port Hamiltonian case, resulting in families ofparameterized reduced order port Hamiltonian approximations.

Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems