IOP Controller Design

IOP equations:

$$A\left[\begin{array}{c}w\\ x\\ \hat{x}\end{array}\right]=b$$

This represents a set of linear equations. A solution exists if $A$ is full rank and ($\#$ columns of $A$) $\ge$ ($\#$ rows of A).

• ($\#$ rows of $A$) = $m+n+(n-\hat{n})$
• ($\#$ columns of $A$) = $2m+\hat{n}$

Then, we need:

$$\begin{array}{rl}2m+\hat{n}& \ge m+n+(n-\hat{n})\\ ⟹m& \ge 2(n-\hat{n})\end{array}$$

We want greater than, not equal to, so that we have more flexibility when designing the controller.