Apologies if this is in the incorrect forum, it seemed the most appropriate from the choices given.

I have a state-space equation of the form

where

are my states,

are my user-defined controls, and

are disturbances to the system, and

,

, and

are appropriately sized matrices.

The problem I have is that certain entries of

are sort of related to others, in that, some terms in the

vector are the same as other terms, but at some time later...so essentially I have a delay in the system, but only on certain elements of

. I can essentially split the

vector into two groups; one group being the disturbance itself, and the other being the same disturbance at some time later.

Is there a way I can include this delay into the system, so that it's of the same form as the first equation I wrote? I can obviously enforce this delay when solving the equation numerically, but I ideally need the matrices to be of this form so that I can use it later for control synthesis.

Any ideas would be welcome.