FPGA Central

For scalar systems we have say a(z^-1)=(1-0.5z^-1)

then

H=a~/a is an all-pass transfer function. Where a~ is z^-1a(z)

Does a similar property hold for polynomial matrices ie

H=A^-1A~

where det(A)=0 has all its roots within the unit circle and det(A~)
has all its roots outside the unit circle.

And here A=A0+A1z^-1+...Anz^-1 is a polynomial matrix with
coefficients of z^-i,i=0,1..n which are all matrices.

ex in analogue we normally have a time-delay exp(-s*tau). We could
have exp(-s*T) wher T is a matrix of delays.
Then we could approx this

exp(sT/2)^-1exp(-sT/2)=[I+sT/2]^-1 * [I-sT/2]

where [I-sT/2] and [I+sT/2] are polynomial matrices in s this time.
(first order - or a pencil!).

Hardy