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-<!-- 2020-11-25 mer. 19:34 -->
+<!-- 2020-11-25 mer. 19:37 -->
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 <title>Robust Control - \(\mathcal{H}_\infty\) Synthesis</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
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@@ -30,29 +30,29 @@
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#orgf9a4c6d">1. Introduction to the Control Methodology - Model Based Control</a></li>
-<li><a href="#org3fca6e1">2. Some Background: From Classical Control to Robust Control</a></li>
-<li><a href="#org2092347">3. The \(\mathcal{H}_\infty\) Norm</a></li>
-<li><a href="#org2331e77">4. \(\mathcal{H}_\infty\) Synthesis</a></li>
-<li><a href="#org9b8faac">5. The Generalized Plant</a></li>
-<li><a href="#org8116ae5">6. Problem Formulation</a></li>
-<li><a href="#org42f9bcf">7. Classical feedback control and closed loop transfer functions</a></li>
-<li><a href="#orgf00feb8">8. From a Classical Feedback Architecture to a Generalized Plant</a></li>
-<li><a href="#org7c94ee9">9. Modern Interpretation of the Control Specifications</a>
+<li><a href="#org4643b2e">1. Introduction to the Control Methodology - Model Based Control</a></li>
+<li><a href="#org8a683c3">2. Some Background: From Classical Control to Robust Control</a></li>
+<li><a href="#orgc683003">3. The \(\mathcal{H}_\infty\) Norm</a></li>
+<li><a href="#org23e7e4a">4. \(\mathcal{H}_\infty\) Synthesis</a></li>
+<li><a href="#orgcd078d9">5. The Generalized Plant</a></li>
+<li><a href="#org675f3d8">6. Problem Formulation</a></li>
+<li><a href="#org64eaa6d">7. Classical feedback control and closed loop transfer functions</a></li>
+<li><a href="#orgee3fbb9">8. From a Classical Feedback Architecture to a Generalized Plant</a></li>
+<li><a href="#orgc9be7b5">9. Modern Interpretation of the Control Specifications</a>
 <ul>
-<li><a href="#orgfcb96b5">9.1. Introduction</a></li>
+<li><a href="#orgf9aaff9">9.1. Introduction</a></li>
 </ul>
 </li>
-<li><a href="#orgc9ce5a6">10. Resources</a></li>
+<li><a href="#org42f3566">10. Resources</a></li>
 </ul>
 </div>
 </div>
 
-<div id="outline-container-orgf9a4c6d" class="outline-2">
-<h2 id="orgf9a4c6d"><span class="section-number-2">1</span> Introduction to the Control Methodology - Model Based Control</h2>
+<div id="outline-container-org4643b2e" class="outline-2">
+<h2 id="org4643b2e"><span class="section-number-2">1</span> Introduction to the Control Methodology - Model Based Control</h2>
 <div class="outline-text-2" id="text-1">
 <p>
-The typical methodology when applying Model Based Control to a plant is schematically shown in Figure <a href="#orgb1a2ae6">1</a>.
+The typical methodology when applying Model Based Control to a plant is schematically shown in Figure <a href="#org3f1eee3">1</a>.
 It consists of three steps:
 </p>
 <ol class="org-ol">
@@ -66,7 +66,7 @@ It consists of three steps:
 </ol>
 
 
-<div id="orgb1a2ae6" class="figure">
+<div id="org3f1eee3" class="figure">
 <p><img src="figs/control-procedure.png" alt="control-procedure.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Typical Methodoly for Model Based Control</p>
@@ -78,8 +78,8 @@ In this document, we will mainly focus on steps 2 and 3.
 </div>
 </div>
 
-<div id="outline-container-org3fca6e1" class="outline-2">
-<h2 id="org3fca6e1"><span class="section-number-2">2</span> Some Background: From Classical Control to Robust Control</h2>
+<div id="outline-container-org8a683c3" class="outline-2">
+<h2 id="org8a683c3"><span class="section-number-2">2</span> Some Background: From Classical Control to Robust Control</h2>
 <div class="outline-text-2" id="text-2">
 <p>
 Classical Control (1930)
@@ -156,10 +156,10 @@ Robust Control (1980)
 </div>
 </div>
 
-<div id="outline-container-org2092347" class="outline-2">
-<h2 id="org2092347"><span class="section-number-2">3</span> The \(\mathcal{H}_\infty\) Norm</h2>
+<div id="outline-container-orgc683003" class="outline-2">
+<h2 id="orgc683003"><span class="section-number-2">3</span> The \(\mathcal{H}_\infty\) Norm</h2>
 <div class="outline-text-2" id="text-3">
-<div class="definition" id="org7770f0d">
+<div class="definition" id="org376138c">
 <p>
 The \(\mathcal{H}_\infty\) norm is defined as the peak of the maximum singular value of the frequency response
 </p>
@@ -176,7 +176,7 @@ For a SISO system \(G(s)\), it is simply the peak value of \(|G(j\omega)|\) as a
 
 </div>
 
-<div class="exampl" id="org5cdde3f">
+<div class="exampl" id="org4a6bc14">
 <p>
 Let&rsquo;s define a plant dynamics:
 </p>
@@ -201,12 +201,12 @@ And compute its \(\mathcal{H}_\infty\) norm using the <code>hinfnorm</code> func
 
 
 <p>
-The magnitude \(|G(j\omega)|\) of the plant \(G(s)\) as a function of frequency is shown in Figure <a href="#orgd616903">2</a>.
+The magnitude \(|G(j\omega)|\) of the plant \(G(s)\) as a function of frequency is shown in Figure <a href="#org109ee6e">2</a>.
 The maximum value of the magnitude over all frequencies does correspond to the \(\mathcal{H}_\infty\) norm of \(G(s)\) as Equation \eqref{eq:hinf_norm_siso} implies.
 </p>
 
 
-<div id="orgd616903" class="figure">
+<div id="org109ee6e" class="figure">
 <p><img src="figs/hinfinity_norm_siso_bode.png" alt="hinfinity_norm_siso_bode.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Example of the \(\mathcal{H}_\infty\) norm of a SISO system</p>
@@ -216,8 +216,8 @@ The maximum value of the magnitude over all frequencies does correspond to the \
 </div>
 </div>
 
-<div id="outline-container-org2331e77" class="outline-2">
-<h2 id="org2331e77"><span class="section-number-2">4</span> \(\mathcal{H}_\infty\) Synthesis</h2>
+<div id="outline-container-org23e7e4a" class="outline-2">
+<h2 id="org23e7e4a"><span class="section-number-2">4</span> \(\mathcal{H}_\infty\) Synthesis</h2>
 <div class="outline-text-2" id="text-4">
 <p>
 <b>Optimization problem</b>:
@@ -246,16 +246,16 @@ The maximum value of the magnitude over all frequencies does correspond to the \
 </div>
 </div>
 
-<div id="outline-container-org9b8faac" class="outline-2">
-<h2 id="org9b8faac"><span class="section-number-2">5</span> The Generalized Plant</h2>
+<div id="outline-container-orgcd078d9" class="outline-2">
+<h2 id="orgcd078d9"><span class="section-number-2">5</span> The Generalized Plant</h2>
 <div class="outline-text-2" id="text-5">
 
-<div id="orgd112ab1" class="figure">
+<div id="org798bc0e" class="figure">
 <p><img src="figs/general_plant.png" alt="general_plant.png" />
 </p>
 </div>
 
-<table id="orgc823a19" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="org8df566a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
 <caption class="t-above"><span class="table-number">Table 1:</span> Notations for the general configuration</caption>
 
 <colgroup>
@@ -303,10 +303,10 @@ The maximum value of the magnitude over all frequencies does correspond to the \
 </div>
 </div>
 
-<div id="outline-container-org8116ae5" class="outline-2">
-<h2 id="org8116ae5"><span class="section-number-2">6</span> Problem Formulation</h2>
+<div id="outline-container-org675f3d8" class="outline-2">
+<h2 id="org675f3d8"><span class="section-number-2">6</span> Problem Formulation</h2>
 <div class="outline-text-2" id="text-6">
-<div class="important" id="org179b25f">
+<div class="important" id="orgaecd7ae">
 <p>
 The \(\mathcal{H}_\infty\) Synthesis objective is to find all stabilizing controllers \(K\) which minimize
 </p>
@@ -317,7 +317,7 @@ The \(\mathcal{H}_\infty\) Synthesis objective is to find all stabilizing contro
 </div>
 
 
-<div id="orgcf0dd39" class="figure">
+<div id="orgc5544e6" class="figure">
 <p><img src="figs/general_control_names.png" alt="general_control_names.png" />
 </p>
 <p><span class="figure-number">Figure 4: </span>General Control Configuration</p>
@@ -326,17 +326,17 @@ The \(\mathcal{H}_\infty\) Synthesis objective is to find all stabilizing contro
 </div>
 
 
-<div id="outline-container-org42f9bcf" class="outline-2">
-<h2 id="org42f9bcf"><span class="section-number-2">7</span> Classical feedback control and closed loop transfer functions</h2>
+<div id="outline-container-org64eaa6d" class="outline-2">
+<h2 id="org64eaa6d"><span class="section-number-2">7</span> Classical feedback control and closed loop transfer functions</h2>
 <div class="outline-text-2" id="text-7">
 
-<div id="orgb1f039f" class="figure">
+<div id="orge2d651d" class="figure">
 <p><img src="figs/classical_feedback.png" alt="classical_feedback.png" />
 </p>
 <p><span class="figure-number">Figure 5: </span>Classical Feedback Architecture</p>
 </div>
 
-<table id="orgfaf4a42" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="org101f1b2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
 <caption class="t-above"><span class="table-number">Table 2:</span> Notations for the Classical Feedback Architecture</caption>
 
 <colgroup>
@@ -390,8 +390,8 @@ The \(\mathcal{H}_\infty\) Synthesis objective is to find all stabilizing contro
 </div>
 </div>
 
-<div id="outline-container-orgf00feb8" class="outline-2">
-<h2 id="orgf00feb8"><span class="section-number-2">8</span> From a Classical Feedback Architecture to a Generalized Plant</h2>
+<div id="outline-container-orgee3fbb9" class="outline-2">
+<h2 id="orgee3fbb9"><span class="section-number-2">8</span> From a Classical Feedback Architecture to a Generalized Plant</h2>
 <div class="outline-text-2" id="text-8">
 <p>
 The procedure is:
@@ -401,13 +401,13 @@ The procedure is:
 <li>Remove \(K\) and rearrange the inputs and outputs</li>
 </ol>
 
-<div class="exampl" id="orgd38b593">
+<div class="exampl" id="orgb5a13ef">
 <p>
-Let&rsquo;s find the Generalized plant of corresponding to the tracking control architecture shown in Figure <a href="#orgaa07663">6</a>
+Let&rsquo;s find the Generalized plant of corresponding to the tracking control architecture shown in Figure <a href="#orge163327">6</a>
 </p>
 
 
-<div id="orgaa07663" class="figure">
+<div id="orge163327" class="figure">
 <p><img src="figs/classical_feedback_tracking.png" alt="classical_feedback_tracking.png" />
 </p>
 <p><span class="figure-number">Figure 6: </span>Classical Feedback Control Architecture (Tracking)</p>
@@ -425,11 +425,11 @@ First, define the signals of the generalized plant:
 
 <p>
 Then, Remove \(K\) and rearrange the inputs and outputs.
-We obtain the generalized plant shown in Figure <a href="#orgb73ca0b">7</a>.
+We obtain the generalized plant shown in Figure <a href="#orgfbdbe4a">7</a>.
 </p>
 
 
-<div id="orgb73ca0b" class="figure">
+<div id="orgfbdbe4a" class="figure">
 <p><img src="figs/mixed_sensitivity_ref_tracking.png" alt="mixed_sensitivity_ref_tracking.png" />
 </p>
 <p><span class="figure-number">Figure 7: </span>Generalized plant of the Classical Feedback Control Architecture (Tracking)</p>
@@ -449,12 +449,12 @@ Using Matlab, the generalized plant can be defined as follows:
 </div>
 </div>
 
-<div id="outline-container-org7c94ee9" class="outline-2">
-<h2 id="org7c94ee9"><span class="section-number-2">9</span> Modern Interpretation of the Control Specifications</h2>
+<div id="outline-container-orgc9be7b5" class="outline-2">
+<h2 id="orgc9be7b5"><span class="section-number-2">9</span> Modern Interpretation of the Control Specifications</h2>
 <div class="outline-text-2" id="text-9">
 </div>
-<div id="outline-container-orgfcb96b5" class="outline-3">
-<h3 id="orgfcb96b5"><span class="section-number-3">9.1</span> Introduction</h3>
+<div id="outline-container-orgf9aaff9" class="outline-3">
+<h3 id="orgf9aaff9"><span class="section-number-3">9.1</span> Introduction</h3>
 <div class="outline-text-3" id="text-9-1">
 <ul class="org-ul">
 <li><b>Reference tracking</b> Overshoot, Static error, Setling time
@@ -488,8 +488,8 @@ Using Matlab, the generalized plant can be defined as follows:
 </div>
 </div>
 
-<div id="outline-container-orgc9ce5a6" class="outline-2">
-<h2 id="orgc9ce5a6"><span class="section-number-2">10</span> Resources</h2>
+<div id="outline-container-org42f3566" class="outline-2">
+<h2 id="org42f3566"><span class="section-number-2">10</span> Resources</h2>
 <div class="outline-text-2" id="text-10">
 <p>
 <iframe width="1280" height="720" src="https://www.youtube.com/embed/?listType=playlist&list=PLn8PRpmsu08qFLMfgTEzR8DxOPE7fBiin" frameborder="0" allowfullscreen></iframe>
@@ -503,7 +503,7 @@ Using Matlab, the generalized plant can be defined as follows:
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-11-25 mer. 19:34</p>
+<p class="date">Created: 2020-11-25 mer. 19:37</p>
 </div>
 </body>
 </html>
diff --git a/index.org b/index.org
index bd50b9f..4b21d25 100644
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@@ -9,11 +9,8 @@
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