Characterization of the moments of a linear system driven by explicit signal generators

The characterization of the moments of a linear system 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 and it is shown that, under specific conditions, the new definition and the one based on the Sylvester equation are equivalent. The results, illustrated by mean of two numerical examples, lay the foundation for the characterization of reduced order models for such a class of input.