Notice that the poles of the system are still the eigenvalues of the
G
matrix. Thus any techniques for placing the poles of the
G
matrix are still valid, except we need to make sure the poles stay within the unit circle for stability instead of the left half plane. If we want to figure out how a system will respond to an input, we can use the final value theorem like we do in CT.
Theorem 15
For a transfer function
G(z)
which has all poles in the unit circle, the final value of
g[n]
is given by
limn=→∞g[n]=limz→1(z−1)G(z).
The other primary difference from CT is that in DT, a pole which is closer to the origin means a faster transient response.