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4 Qualifying Exam/2 Writing/2. QE State of the Art.md
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@ -38,4 +38,6 @@ The other type of uncertainty considered is unstructured uncertainty. This type
$$ \tilde P = (1+\Delta W_2) P $$ $$ \tilde P = (1+\Delta W_2) P $$
Where $\Delta$ is a variable stable transfer function with $||\Delta||_\infty < 1$, and $W_2$ is the uncertainty profile. Where $\Delta$ is a variable stable transfer function with $||\Delta||_\infty < 1$, and $W_2$ is the uncertainty profile.
The 'disk' part of the multiplicative disk uncertainty comes from analysis in the complex domain, specifically looking at the Nyquist Stability Criterion. Stability according to this criterion is determined when the loop gain $L$ of a system does not pass through the point -1 during a sweep of all frequencies on the imaginary access. For robust stability, we examine if a system is still stable when calculating the Nyquist plot of $W_2 L$. The 'disk' part of the multiplicative disk uncertainty comes from analysis in the complex domain, specifically looking at the Nyquist Stability Criterion. Stability according to this criterion is determined when the loop gain $L$ of a system does not pass through the point -1 during a sweep of all frequencies on the imaginary access. For robust stability, we examine if a system is still stable when calculating the Nyquist plot of $W_2 L$. If it is, then all perturbed plants $\tilde P = (1+\Delta W_2)P$ are also stable.
This is useful for us. If we can find an uncertainty transfer function $W_2$ that we are satisfied with,