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Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems. (English) Zbl 1364.93113

Summary: In this paper we propose a solution to the problem of moment matching with preservation of the port Hamiltonian structure, in the framework of time-domain moment matching. We characterize several families of parameterized port Hamiltonian models that match the moments of a given port Hamiltonian system, at a set of finite interpolation points. We also discuss the problem of Markov parameters matching for linear systems as a moment matching problem for descriptor representations associated with the given system, at zero interpolation points. Solving this problem yields families of parameterized reduced order models that achieve Markov parameter matching. Finally, we apply these results to the port Hamiltonian case, resulting in families of parameterized reduced order port Hamiltonian approximations.

MSC:

93B11 System structure simplification
70H08 Nearly integrable Hamiltonian systems, KAM theory
93C05 Linear systems in control theory
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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