Moment Matching for Nonlinear Systems of Second-Order Equations

In this paper we consider the problem of constructing nonlinear systems of second-order equations that achieve moment matching. In particular, necessary and sufficient conditions are given for which a system of second-order equations achieves moment matching, and a family of systems of second-order equations achieving moment matching is directly constructed by extracting it, via particular choices of the free mappings, from a parameterization of all systems achieving moment matching. The results are specialized for the scenario in which the signal generator is a linear system. Finally, the results of the paper are demonstrated by constructing reduced order models of a two link robotic manipulator in the second-order equation form.