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title = "Systems and Signals Norms"
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author = ["Thomas Dehaeze"]
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draft = false
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2020-08-17 23:00:20 +02:00
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### Backlinks {#backlinks}
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- [Multivariable Control]({{< relref "multivariable_control" >}})
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Tags
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Resources:
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- ([Skogestad and Postlethwaite 2007](#org533c8de))
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- ([Toivonen 2002](#orgb393f10))
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- ([Zhang 2011](#org1ea8e81))
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## \\(\mathcal{H}\_\infty\\) Norm {#mathcal-h-infty--norm}
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SISO Systems => absolute value => bode plot
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MIMO Systems => singular value
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Signal
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## \\(\mathcal{H}\_2\\) Norm {#mathcal-h-2--norm}
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RMS value
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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](#org5e40c21)), 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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## Link between signal and system norms {#link-between-signal-and-system-norms}
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## Bibliography {#bibliography}
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<a id="org5e40c21"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
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<a id="org533c8de"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
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<a id="orgb393f10"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
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<a id="org1ea8e81"></a>Zhang, Weidong. 2011. _Quantitative Process Control Theory_. CRC Press.
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