transform of
the impulse response:
The transfer function can be defined as the
transform of
the impulse response:
![$\displaystyle H(z) \isdef \sum_{n=0}^{\infty} h(n) z^{-n}
= D + \sum_{n=1}^{\infty} \left(C A^{n-1} B \right) z^{-n}
= D + z^{-1}C \left[\sum_{n=0}^{\infty} \left(z^{-1}A\right)^n\right] B
$](img2113.png)
Using the closed-form sum of a matrix geometric series,G.4we obtain
inputs and 
outputs, 
is a 
transfer-function matrix
(or ``matrix transfer function'').
