Originally Posted by

**Guffmeister** 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

$\displaystyle \dot{x} = Ax + Bu + Ew$

where $\displaystyle x \in \mathbb{R}^n$ are my states, $\displaystyle u \in \mathbb{R}^m$ are my user-defined controls, and $\displaystyle w \in \mathbb{R}^p$ are disturbances to the system, and $\displaystyle A$, $\displaystyle B$, and $\displaystyle C$ are appropriately sized matrices.

The problem I have is that certain entries of $\displaystyle w$ are sort of related to others, in that, some terms in the $\displaystyle w$ 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 $\displaystyle w$. I can essentially split the $\displaystyle w$ 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.