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4 Qualifying Exam/3 Notes/Feedback Control Theory.md
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@ -93,6 +93,8 @@ W_2 is basically a transfer function that will always be greater in magnitude th
>> A system is robustly stable if it is internally stable for every plant in the set $\mathcal{P}$: >> A system is robustly stable if it is internally stable for every plant in the set $\mathcal{P}$:
>> $$|| \Delta W_2 T ||_\infty < 1$$ >> $$|| \Delta W_2 T ||_\infty < 1$$
>> ![[Pasted image 20241015172652.png]] >> ![[Pasted image 20241015172652.png]]
>> Nominal performance is achieved simultaneously when
>> $$ || \text{max} (|W_1S|, |W_2 T|)||_\infty < 1$$>
> >
>>[!important] Robust Performance >>[!important] Robust Performance
>>$$ |||W_1 S | + |W_2 T| ||_\infty < 1 $$ >>$$ |||W_1 S | + |W_2 T| ||_\infty < 1 $$