The matrix is the state transition matrix. The vector holds the state variables that determine the state of the system at time . The order of a state-space system is equal to the number of state variables, i.e., the dimensionality of . The input and output signals have been trivially redefined as
to follow normal convention for 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 because tools for state-space analysis are well known and included in many software libraries such as with matlab.
Single-Input, Single-Output (SISO) FDN
Time Varying Comb Filters