When
, the FDN in Fig. 1.22 reduces to a standard
state-space description [426, Appendix E] for a
three-input, three-output, order 3 system:
in order to obtain standard state-space form.
Thus, an FDN can be viewed as a generalized state-space model for a class of th-order linear systems--``generalized'' in the sense that unit delays are replaced by arbitrary delays. This correspondence is valuable for analysis since tools for state-space analysis are well known (and included in software such as Matlab, among others).
An introduction to state-space models is given in [426, available online]. A more detailed treatment appears in [204].