6. Realization

The realization consists in building a system with a given transfer function G or, what amounts to the same thing, which transforms a certain input into an imposed output. In practice, the G matrix is known only through the results of experimental input-output measurements. The solution to the realization problem depends on the type of information about G. This information may be the algebraic expression of some of the elements of G, or its serial development in the vicinity of certain points, or its first Markov parameters, or its first moments, or its value at certain points.

A distinction needs to be made between realization theory, where a system of the same dimension as the initial system is sought, and model reduction (see §