digital-brain/content/zettels/norms.md

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title = "Systems and Signals Norms"
author = ["Thomas Dehaeze"]
draft = false
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Backlinks:
- [Multivariable Control]({{< relref "multivariable_control" >}})
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Tags
:
Resources:
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- ([Skogestad and Postlethwaite 2007](#org140f9cc))
- ([Toivonen 2002](#orgc1385a9))
- ([Zhang 2011](#org8471dd8))
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## \\(\mathcal{H}\_\infty\\) Norm {#mathcal-h-infty--norm}
SISO Systems => absolute value => bode plot
MIMO Systems => singular value
Signal
## \\(\mathcal{H}\_2\\) Norm {#mathcal-h-2--norm}
The \\(\mathcal{H}\_2\\) is very useful when combined to [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}}).
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As explained in ([Monkhorst 2004](#orgafef987)), the \\(\mathcal{H}\_2\\) norm has a stochastic interpretation:
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> The squared \\(\mathcal{H}\_2\\) norm can be interpreted as the output variance of a system with zero mean white noise input.
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Minimizing the \\(\mathcal{H}\_2\\) norm can be equivalent as minimizing the RMS value of some signals in the system.
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## Link between signal and system norms {#link-between-signal-and-system-norms}
## Bibliography {#bibliography}
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<a id="orgafef987"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
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<a id="org140f9cc"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
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<a id="orgc1385a9"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
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<a id="org8471dd8"></a>Zhang, Weidong. 2011. _Quantitative Process Control Theory_. CRC Press.