How to divide transfer functions with delay?

I want to make the division operation between the following transfer functions:

g12 = tf(-18.9,[21 1],'ioDelay',3)
g11 = tf(12.8,[16.7 1],'ioDelay',1)

Everytime I try to divide g12/g11, I get an error that says

Error using  /  (line xx)
In "SYS1/SYS2", SYS2 must be delay free.

How can I get this right?

Thank you.

[Vasumathi Raman]

Have you found the solution? I am also facing the same while designing decoupler. Thanks in advance.

[Walter Roberson]

What does it mean to divide delays? Do you really want it to mean the difference in delays?

Answer 1

[Walter Roberson]

If you do a straight algebraic division of the formulas including delays, then you would end up with a term exp(-3*s)/exp(-1*s) = exp(-2*s) implying a delay of 2 somehow arising from dividing a system with delay 3 by a system with delay 1.

I do not really know what it means to divide delays, but I would tend to expect that the resulting system would have a delay which was either the least common multiple of the delays or else the maximum of the delays, not the difference in the delays.