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+++ title = "Systems and Signals Norms" author = ["Thomas Dehaeze"] draft = false +++
Backlinks
- [Multivariable Control]({{< relref "multivariable_control" >}})
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\(\mathcal{H}_\infty\) Norm
SISO Systems => absolute value => bode plot MIMO Systems => singular value Signal
\(\mathcal{H}_2\) Norm
RMS value
The \(\mathcal{H}_2\) is very useful when combined to [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}}).
As explained in (Monkhorst 2004), 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.
Link between signal and system norms
Bibliography
Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
Skogestad, Sigurd, and Ian Postlethwaite. 2007. Multivariable Feedback Control: Analysis and Design. John Wiley.
Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
Zhang, Weidong. 2011. Quantitative Process Control Theory. CRC Press.