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4 Qualifying Exam/2 Writing/2. QE State of the Art.md
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@ -44,4 +44,4 @@ This is useful for us. If we can find an uncertainty transfer function $W_2$ tha
$\Delta$ is almost always considered a free variable transfer function. Since $||\Delta||_\infty < 1 \text{ } \forall \omega$, $\Delta$ will not decrease the minimum robustness margin. This is fine for developing a controller, but when it comes to actually verifying robustness of a controller implementation, $\Delta$ cannot be a variable. To create a plant to simulate a perturbed plant, $\Delta$ must have an expression. $\Delta$ is almost always considered a free variable transfer function. Since $||\Delta||_\infty < 1 \text{ } \forall \omega$, $\Delta$ will not decrease the minimum robustness margin. This is fine for developing a controller, but when it comes to actually verifying robustness of a controller implementation, $\Delta$ cannot be a variable. To create a plant to simulate a perturbed plant, $\Delta$ must have an expression.
**Limitation**: *There is no current method for creating random examples of $\Delta$.* **Limitation**: *There is no current method for creating random examples of $\Delta$.* Because of this, it is not currently possible to test implementations of controllers against unstructured perturbations.