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Thomas Dehaeze 2020-08-17 23:19:44 +02:00
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content/zettels/norms.md
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### Backlinks {#backlinks} Backlinks:
- [Multivariable Control]({{< relref "multivariable_control" >}}) - [Multivariable Control]({{< relref "multivariable_control" >}})
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Resources: Resources:
- ([Skogestad and Postlethwaite 2007](#org533c8de)) - ([Skogestad and Postlethwaite 2007](#org140f9cc))
- ([Toivonen 2002](#orgb393f10)) - ([Toivonen 2002](#orgc1385a9))
- ([Zhang 2011](#org1ea8e81)) - ([Zhang 2011](#org8471dd8))
## \\(\mathcal{H}\_\infty\\) Norm {#mathcal-h-infty--norm} ## \\(\mathcal{H}\_\infty\\) Norm {#mathcal-h-infty--norm}
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## \\(\mathcal{H}\_2\\) Norm {#mathcal-h-2--norm} ## \\(\mathcal{H}\_2\\) Norm {#mathcal-h-2--norm}
RMS value
The \\(\mathcal{H}\_2\\) is very useful when combined to [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}}). The \\(\mathcal{H}\_2\\) is very useful when combined to [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}}).
As explained in ([Monkhorst 2004](#org5e40c21)), the \\(\mathcal{H}\_2\\) norm has a stochastic interpretation: As explained in ([Monkhorst 2004](#orgafef987)), the \\(\mathcal{H}\_2\\) norm has a stochastic interpretation:
> The squared \\(\mathcal{H}\_2\\) norm can be interpreted as the output variance of a system with zero mean white noise input. > The squared \\(\mathcal{H}\_2\\) norm can be interpreted as the output variance of a system with zero mean white noise input.
Minimizing the \\(\mathcal{H}\_2\\) norm can be equivalent as minimizing the RMS value of some signals in the system.
## Link between signal and system norms {#link-between-signal-and-system-norms} ## Link between signal and system norms {#link-between-signal-and-system-norms}
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org5e40c21"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University. <a id="orgafef987"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
<a id="org533c8de"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley. <a id="org140f9cc"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orgb393f10"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University. <a id="orgc1385a9"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
<a id="org1ea8e81"></a>Zhang, Weidong. 2011. _Quantitative Process Control Theory_. CRC Press. <a id="org8471dd8"></a>Zhang, Weidong. 2011. _Quantitative Process Control Theory_. CRC Press.