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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.
Link between signal and system norms
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, . ↩
Backlinks
- [Multivariable Control]({{< relref "multivariable_control" >}})