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diff --git a/.nojekyll b/.nojekyll
@@ -1 +1 @@
-b940995b
+f7af3563
diff --git a/classes_PWA 18.html b/classes_PWA 18.html
diff --git a/classes_reset 18.html b/classes_reset 18.html
diff --git a/classes_reset.html b/classes_reset.html
diff --git a/classes_switched 19.html b/classes_switched 19.html
diff --git a/classes_switched.html b/classes_switched.html
diff --git a/complementarity_simulations 17.html b/complementarity_simulations 17.html
diff --git a/complementarity_simulations.html b/complementarity_simulations.html
diff --git a/complementarity_software 14.html b/complementarity_software 14.html
diff --git a/des 15.html b/des 15.html
diff --git a/des_automata.html b/des_automata.html
@@ -2137,16 +2137,16 @@ <h3 class="anchored" data-anchor-id="mealy-machine">Mealy machine</h3>
 <span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a><span class="pp">@show</span> <span class="fu">update!</span>(dtr), <span class="fu">output</span>(dtr)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </details>
 <div class="cell-output cell-output-stdout">
-<pre><code>x_initial = rand(0:k, n) = [1, 2, 3, 2]
+<pre><code>x_initial = rand(0:k, n) = [4, 0, 3, 2]
 output(dtr) = [0, 1, 1, 1]
-(update!(dtr), output(dtr)) = ([1, 1, 2, 3], [0, 0, 1, 1])
-(update!(dtr), output(dtr)) = ([1, 1, 1, 2], [0, 0, 0, 1])
-(update!(dtr), output(dtr)) = ([1, 1, 1, 1], [1, 0, 0, 0])
-(update!(dtr), output(dtr)) = ([2, 1, 1, 1], [0, 1, 0, 0])
-(update!(dtr), output(dtr)) = ([2, 2, 1, 1], [0, 0, 1, 0])</code></pre>
+(update!(dtr), output(dtr)) = ([4, 4, 0, 3], [0, 0, 1, 1])
+(update!(dtr), output(dtr)) = ([4, 4, 4, 0], [0, 0, 0, 1])
+(update!(dtr), output(dtr)) = ([4, 4, 4, 4], [1, 0, 0, 0])
+(update!(dtr), output(dtr)) = ([1, 4, 4, 4], [0, 1, 0, 0])
+(update!(dtr), output(dtr)) = ([1, 1, 4, 4], [0, 0, 1, 0])</code></pre>
 </div>
 <div class="cell-output cell-output-display" data-execution_count="1">
-<pre><code>([2, 2, 1, 1], [0, 0, 1, 0])</code></pre>
+<pre><code>([1, 1, 4, 4], [0, 0, 1, 0])</code></pre>
 </div>
 </div>
 <p>We can see that although initially the there can be more tokens, after a few iterations the algorithm achieves the goal of having just one token in the ring.</p>

diff --git a/des_references 16.html b/des_references 16.html
diff --git a/des_software 13.html b/des_software 13.html
diff --git a/hybrid_automata_references 17.html b/hybrid_automata_references 17.html
diff --git a/hybrid_equations 20.html b/hybrid_equations 20.html
diff --git a/hybrid_equations.html b/hybrid_equations.html
diff --git a/hybrid_system_course_mindmap 3.html b/hybrid_system_course_mindmap 3.html
diff --git a/max_plus_algebra 17.html b/max_plus_algebra 17.html
diff --git a/max_plus_algebra.html b/max_plus_algebra.html
diff --git a/max_plus_references 15.html b/max_plus_references 15.html
diff --git a/max_plus_software 15.html b/max_plus_software 15.html
diff --git a/mld_logic_vs_inequalities 2.html b/mld_logic_vs_inequalities 2.html
diff --git a/mld_mld_and_pwa.html b/mld_mld_and_pwa.html
diff --git a/mpc_mld_explicit.html b/mpc_mld_explicit.html
diff --git a/petri_nets 15.html b/petri_nets 15.html
diff --git a/search.json b/search.json
diff --git a/sitemap.xml b/sitemap.xml
@@ -6,7 +6,7 @@
   </url>
   <url>
     <loc>https://hurak.github.io/hys/mld_mld_and_pwa.html</loc>
-    <lastmod>2024-12-23T21:38:31.069Z</lastmod>
+    <lastmod>2025-01-10T12:48:54.944Z</lastmod>
   </url>
   <url>
     <loc>https://hurak.github.io/hys/petri_nets_references.html</loc>
@@ -94,7 +94,7 @@
   </url>
   <url>
     <loc>https://hurak.github.io/hys/mld_logic_vs_inequalities.html</loc>
-    <lastmod>2024-12-23T21:17:03.904Z</lastmod>
+    <lastmod>2025-01-10T10:03:03.056Z</lastmod>
   </url>
   <url>
     <loc>https://hurak.github.io/hys/stability_via_common_lyapunov_function.html</loc>

diff --git a/solution_references 17.html b/solution_references 17.html
diff --git a/solution_types 14.html b/solution_types 14.html
diff --git a/stability_references 10.html b/stability_references 10.html
diff --git a/stability_via_common_lyapunov_function 15.html b/stability_via_common_lyapunov_function 15.html
diff --git a/stability_via_multiple_lyapunov_function.html b/stability_via_multiple_lyapunov_function.html
@@ -762,6 +762,14 @@ <h1 class="title">Stability via multiple Lyapunov functions</h1>
 <span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>constraints <span class="op">=</span> [constraint₁, constraint₂]</span>
 <span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a>problem <span class="op">=</span> <span class="fu">satisfy</span>(constraints)</span>
 <span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a><span class="fu">solve!</span>(problem,SCS.Optimizer,silent<span class="op">=</span><span class="cn">true</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>Precompiling Convex...
+   2573.1 ms  ✓ Convex
+  1 dependency successfully precompiled in 3 seconds. 65 already precompiled.
+Precompiling SCS...
+   1320.7 ms  ✓ SCS
+  1 dependency successfully precompiled in 1 seconds. 66 already precompiled.</code></pre>
+</div>
 <div class="cell-output cell-output-display" data-execution_count="1">
 <pre><code>Problem statistics
   problem is DCP         : true
@@ -790,7 +798,7 @@ <h1 class="title">Stability via multiple Lyapunov functions</h1>
    │     └─ Convex.NegateAtom (affine; real)
    │        └─ …
    ├─ PSD constraint (convex)
-   │  └─ 2×2 real variable (id: 498…659)
+   │  └─ 2×2 real variable (id: 170…837)
    ⋮</code></pre>
 </div>
 </div>
@@ -812,23 +820,23 @@ <h1 class="title">Stability via multiple Lyapunov functions</h1>
 </div>
 <p>The conclusion about the imposibility to find a single quadratic Lyapunov function for both subsystems is also suppported by plotting the invariant sets for the two subsystems. First, we need to compute Lyapunov functions for the two subsystems.</p>
 <div id="10" class="cell" data-execution_count="1">
-<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>X₁ <span class="op">=</span> <span class="fu">Semidefinite</span>(<span class="fl">2</span>)</span>
-<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>constraint₁ <span class="op">=</span> A₁<span class="ch">'*X₁ + X₁*A₁ ⪯ -Matrix{Float64}(I, 2, 2)</span></span>
-<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>problem₁ <span class="op">=</span> <span class="fu">satisfy</span>(constraint₁)</span>
-<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="fu">solve!</span>(problem₁,SCS.Optimizer,silent<span class="op">=</span><span class="cn">true</span>)</span>
-<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>X₁.value</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>X₁ <span class="op">=</span> <span class="fu">Semidefinite</span>(<span class="fl">2</span>)</span>
+<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>constraint₁ <span class="op">=</span> A₁<span class="ch">'*X₁ + X₁*A₁ ⪯ -Matrix{Float64}(I, 2, 2)</span></span>
+<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>problem₁ <span class="op">=</span> <span class="fu">satisfy</span>(constraint₁)</span>
+<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="fu">solve!</span>(problem₁,SCS.Optimizer,silent<span class="op">=</span><span class="cn">true</span>)</span>
+<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>X₁.value</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-display" data-execution_count="1">
 <pre><code>2×2 Matrix{Float64}:
  423.71     12.5739
   12.5739  212.123</code></pre>
 </div>
 </div>
 <div id="12" class="cell" data-execution_count="1">
-<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>X₂ <span class="op">=</span> <span class="fu">Semidefinite</span>(<span class="fl">2</span>)</span>
-<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>constraint₂ <span class="op">=</span> A₂<span class="ch">'*X₂ + X₂*A₂ ⪯ -Matrix{Float64}(I, 2, 2)</span></span>
-<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>problem₂ <span class="op">=</span> <span class="fu">satisfy</span>(constraint₂)</span>
-<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="fu">solve!</span>(problem₂,SCS.Optimizer,silent<span class="op">=</span><span class="cn">true</span>)</span>
-<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a>X₂.value</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>X₂ <span class="op">=</span> <span class="fu">Semidefinite</span>(<span class="fl">2</span>)</span>
+<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>constraint₂ <span class="op">=</span> A₂<span class="ch">'*X₂ + X₂*A₂ ⪯ -Matrix{Float64}(I, 2, 2)</span></span>
+<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>problem₂ <span class="op">=</span> <span class="fu">satisfy</span>(constraint₂)</span>
+<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="fu">solve!</span>(problem₂,SCS.Optimizer,silent<span class="op">=</span><span class="cn">true</span>)</span>
+<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a>X₂.value</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-display" data-execution_count="1">
 <pre><code>2×2 Matrix{Float64}:
  212.123   -12.5739
@@ -839,15 +847,15 @@ <h1 class="title">Stability via multiple Lyapunov functions</h1>
 <div id="cell-fig-no-cqlf-with-lyapunov-invariant-sets" class="cell" data-execution_count="1">
 <details class="code-fold">
 <summary>Show the code</summary>
-<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>x1s <span class="op">=</span> <span class="fu">LinRange</span>(<span class="op">-</span><span class="fl">2</span>, <span class="fl">2</span>, <span class="fl">100</span>)</span>
-<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>x2s <span class="op">=</span> <span class="fu">LinRange</span>(<span class="op">-</span><span class="fl">2</span>, <span class="fl">2</span>, <span class="fl">100</span>)</span>
-<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="fu">V₁</span>(x) <span class="op">=</span> x<span class="op">'*</span>X₁.value<span class="op">*</span>x</span>
-<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a><span class="fu">V₂</span>(x) <span class="op">=</span> x<span class="op">'*</span>X₂.value<span class="op">*</span>x</span>
-<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>V1s <span class="op">=</span> [<span class="fu">V₁</span>([x₁,x₂]) for x₁ <span class="kw">in</span> x1s, x₂ <span class="kw">in</span> x2s]</span>
-<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a>V2s <span class="op">=</span> [<span class="fu">V₂</span>([x₁,x₂]) for x₁ <span class="kw">in</span> x1s, x₂ <span class="kw">in</span> x2s]</span>
-<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a><span class="fu">contour!</span>(x1s, x2s, V1s, levels<span class="op">=</span>[<span class="fl">300.0</span>], linewidth<span class="op">=</span><span class="fl">3</span>, color<span class="op">=:</span>blue)</span>
-<span id="cb11-8"><a href="#cb11-8" aria-hidden="true" tabindex="-1"></a><span class="fu">contour!</span>(x1s, x2s, V2s, levels<span class="op">=</span>[<span class="fl">300.0</span>], linewidth<span class="op">=</span><span class="fl">3</span>, color<span class="op">=:</span>green)</span>
-<span id="cb11-9"><a href="#cb11-9" aria-hidden="true" tabindex="-1"></a>fig</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>x1s <span class="op">=</span> <span class="fu">LinRange</span>(<span class="op">-</span><span class="fl">2</span>, <span class="fl">2</span>, <span class="fl">100</span>)</span>
+<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>x2s <span class="op">=</span> <span class="fu">LinRange</span>(<span class="op">-</span><span class="fl">2</span>, <span class="fl">2</span>, <span class="fl">100</span>)</span>
+<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a><span class="fu">V₁</span>(x) <span class="op">=</span> x<span class="op">'*</span>X₁.value<span class="op">*</span>x</span>
+<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a><span class="fu">V₂</span>(x) <span class="op">=</span> x<span class="op">'*</span>X₂.value<span class="op">*</span>x</span>
+<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>V1s <span class="op">=</span> [<span class="fu">V₁</span>([x₁,x₂]) for x₁ <span class="kw">in</span> x1s, x₂ <span class="kw">in</span> x2s]</span>
+<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>V2s <span class="op">=</span> [<span class="fu">V₂</span>([x₁,x₂]) for x₁ <span class="kw">in</span> x1s, x₂ <span class="kw">in</span> x2s]</span>
+<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a><span class="fu">contour!</span>(x1s, x2s, V1s, levels<span class="op">=</span>[<span class="fl">300.0</span>], linewidth<span class="op">=</span><span class="fl">3</span>, color<span class="op">=:</span>blue)</span>
+<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a><span class="fu">contour!</span>(x1s, x2s, V2s, levels<span class="op">=</span>[<span class="fl">300.0</span>], linewidth<span class="op">=</span><span class="fl">3</span>, color<span class="op">=:</span>green)</span>
+<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a>fig</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </details>
 <div class="cell-output cell-output-display" data-execution_count="1">
 <div id="fig-no-cqlf-with-lyapunov-invariant-sets" class="quarto-float quarto-figure quarto-figure-center anchored">