digital-brain/content/zettels/norms.md
2020-06-03 22:43:54 +02:00

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+++ title = "Systems and Signals Norms" author = ["Thomas Dehaeze"] draft = false +++

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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 @phdthesis{monkhorst04_dynam_error_budget, author = {Wouter Monkhorst}, school = {Delft University}, title = {Dynamic Error Budgeting, a design approach}, year = 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.

Bibliography

Skogestad, S., & Postlethwaite, I., Multivariable feedback control: analysis and design (2007), : John Wiley.

Toivonen, H. T. (2002). Robust Control Methods. Retrieved from . .

Zhang, W., Quantitative Process Control Theory (2011), : CRC Press.

Monkhorst, W., Dynamic error budgeting, a design approach (Doctoral dissertation) (2004). Delft University, .

  • [Multivariable Control]({{< relref "multivariable_control" >}})