From f92cc1c58cc37a0e058094c4e2a8f4069b63086f Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 21 Sep 2020 17:03:45 +0200 Subject: [PATCH] Update Content - 2020-09-21 --- content/zettels/singular_value_decomposition.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/content/zettels/singular_value_decomposition.md b/content/zettels/singular_value_decomposition.md index 46f769d..1b7c0cc 100644 --- a/content/zettels/singular_value_decomposition.md +++ b/content/zettels/singular_value_decomposition.md @@ -10,6 +10,8 @@ Tags ## SVD of a MIMO system {#svd-of-a-mimo-system} +This is taken from the book [Multivariable feedback control: analysis and design]({{< relref "skogestad07_multiv_feedb_contr" >}}). + 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. \begin{equation} @@ -45,7 +47,7 @@ We define \\(u\_1 = \bar{u}\\), \\(v\_1 = \bar{v}\\), \\(u\_k=\ubar{u}\\) and \\ ## SVD to pseudo inverse rectangular matrices {#svd-to-pseudo-inverse-rectangular-matrices} -This is taken from [Singular Value Decomposition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}}). +This is taken from the book [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}}). 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 \\]