Merge pull request #330 from dionysos-dev/bl/b1b2

Clarify b1 and b2 in DC-DC example

Author: adrienbanse

docs/src/examples/solvers/DC-DC converter.jl

@@ -16,7 +16,7 @@ using Test     #src
 # ```
 # with
 # ```math
-# A_1 = \begin{bmatrix} -\frac{r_l}{x_l} &0 \\ 0 & -\frac{1}{x_c}\frac{1}{r_0+r_c}  \end{bmatrix}, A_2= \begin{bmatrix} -\frac{1}{x_l}\left(r_l+\frac{r_0r_c}{r_0+r_c}\right) & -\frac{1}{x_l}\frac{r_0}{r_0+r_c}  \\ \frac{1}{x_c}\frac{r_0}{r_0+r_c}   & -\frac{1}{x_c}\frac{1}{r_0+r_c}  \end{bmatrix}, b = \begin{bmatrix} \frac{v_s}{x_l}\\0\end{bmatrix}.
+# A_1 = \begin{bmatrix} -\frac{r_l}{x_l} &0 \\ 0 & -\frac{1}{x_c}\frac{1}{r_0+r_c}  \end{bmatrix}, A_2= \begin{bmatrix} -\frac{1}{x_l}\left(r_l+\frac{r_0r_c}{r_0+r_c}\right) & -\frac{1}{x_l}\frac{r_0}{r_0+r_c}  \\ \frac{1}{x_c}\frac{r_0}{r_0+r_c}   & -\frac{1}{x_c}\frac{1}{r_0+r_c}  \end{bmatrix}, b_1 = b_2 = \begin{bmatrix} \frac{v_s}{x_l}\\0\end{bmatrix}.
 # ```
 # The goal is to design a controller to keep the state of the system in a safety region around the reference desired value, using as input only the switching
 # signal. In order to study the concrete system and its symbolic abstraction in a unified framework, we will solve the problem