Model Reduction by Matching the Steady-State Response of Explicit Signal Generators

Model reduction by moment matching for “interpolation signals” which do not have an implicit model, i.e., they do not satisfy a differential equation, is considered. Particular attention is devoted to discontinuous, possibly periodic, signals. The notion of moment is reformulated using an integral matrix equation. It is shown that, under specific conditions, the new definition and the one based on the Sylvester equation are equivalent. New parameterized families of models achieving moment matching are given. The results are illustrated by means of a numerical example.