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4
4 Qualifying Exam/2 Writing/2. QE State of the Art.md
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@ -27,7 +27,9 @@ $$ \mathcal{P} = \left\{ \frac{1}{(m+e_m)s^2 + (b+e_b)s + (k + e_k)} \right\} \t
\matrix{m_{min} \leq m+e_m \leq m_{max} \\ \matrix{m_{min} \leq m+e_m \leq m_{max} \\
b_{min} \leq b +e_b \leq b_{max} \\ b_{min} \leq b +e_b \leq b_{max} \\
k_{min} \leq k +e_k \leq k_{max}} $$ k_{min} \leq k +e_k \leq k_{max}} $$
where $e_m$ is the difference between the nominal mass and the actual as-built mass. $e_b$ and $e_k$ follow similar logic. Structured perturbations are easy to use to create perturbed plants: simply pick values for $e_m$, $e_b$, and $e_k$ that are within the allowable bounds and plug them in to create a new, perturbed transfer function. where $e_m$ is the difference between the nominal mass and the actual as-built mass. $e_b$ and $e_k$ follow similar logic. Structured perturbations are easy to use to create perturbed plants: simply pick values for $e_m$, $e_b$, and $e_k$ that are within the allowable bounds and plug them in to create a new, perturbed transfer function.
Structured perturbations allow for sampling of the set, but they do have a significant drawback. Structured perturbations severely restrict
Structured perturbations do suffer from a limit Structured perturbations do suffer from a limit
(The disk multiplicative perturbation) (The disk multiplicative perturbation)