### FDN and State Space Descriptions

When in Eq.(2.10), the FDN (Fig.2.28) reduces to a normal state-space model1.3.7),

 (3.11)

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.

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