tdehaeze/digital-brain
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Content - 2020-10-15

Browse Source
This commit is contained in:
Thomas Dehaeze
2020-10-15 21:36:53 +02:00
parent f1cad23157
commit f1c89b14f6
113 changed files with 834 additions and 786 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
content/zettels/singular_value_decomposition.md
View File

@@ -10,7 +10,7 @@ Tags
## SVD of a MIMO system {#svd-of-a-mimo-system}
This is taken from ([Skogestad and Postlethwaite 2007](#org4953f60)).
This is taken from ([Skogestad and Postlethwaite 2007](#orga80f5ed)).
We are interested by the physical interpretation of the SVD when applied to the frequency response of a MIMO system \\(G(s)\\) with \\(m\\) inputs and \\(l\\) outputs.
@@ -43,7 +43,7 @@ Then is follows that:
## SVD to pseudo inverse rectangular matrices {#svd-to-pseudo-inverse-rectangular-matrices}
This is taken from ([Preumont 2018](#org6558f35)).
This is taken from ([Preumont 2018](#orgb521567)).
The **Singular Value Decomposition** (SVD) is a generalization of the eigenvalue decomposition of a rectangular matrix:
\\[ J = U \Sigma V^T = \sum\_{i=1}^r \sigma\_i u\_i v\_i^T \\]
@@ -65,6 +65,6 @@ This will have usually little impact of the fitting error while reducing conside
## Bibliography {#bibliography}
<a id="org6558f35"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="orgb521567"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="org4953f60"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orga80f5ed"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.