7. Model reduction

The purpose of model reduction is to find a realization of dimension k < n. In this case, of course, the transfer function G is not exactly found, but only approximated in some sense. We are therefore looking for an approximation of the rational fraction G by another rational fraction with smaller degrees, which gives this question its name. Model reduction is related to partial realization and Padé approximation. It is very important in practice and implemented when the system is too large to be easily simulated, or when the controller design is too complex or costly. The basic idea behind model reduction is to eliminate states that are poorly controllable and/or observable and therefore have only a limited effect on the system's input-output.

There are many model reduction techniques, each with its own advantages and disadvantages. The choice of technique depends...