Ecuaciones - 01

\[ \begin{align}\begin{aligned}\dot{x}_1 = x_1 - x_1 x_2 - 0.4 x_1 u_1\\\dot{x}_2 = -x_2 + x_1 x_2 - 0.2 x_2 u_2\end{aligned}\end{align} \]

\[\begin{split} \begin{pmatrix} \dot{x}_1 \\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} 1 & -x_1 \\ x_2 & -1 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \end{pmatrix} - \begin{pmatrix} 0.4u_1 & 0 \\ 0 & 0.2 u_2 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \end{pmatrix}\end{split}\]

\[ \begin{align}\begin{aligned}\dot{p}_1 = -x_1 - (p_1 - p_1 x_2 + p_2 x_2 - 0.4 p_1 u_1)\\\dot{p}_2 = x_2 - (-p_2 + p_2 x_1 - p_1 x_1 - 0.2 p_2 u_2)\end{aligned}\end{align} \]

\[\begin{split}\begin{pmatrix} \dot{p}_1 \\ \dot{p}_2 \end{pmatrix} = \begin{pmatrix} -x_1 \\ x_2 \end{pmatrix} - \left[ \begin{pmatrix} 1 & x_2 \\ -x_1 & -1 \end{pmatrix} \begin{pmatrix} p_1 \\ p_2 \end{pmatrix} - \begin{pmatrix} x_2 + 0.4u_1 & 0 \\ 0 & -x_1 + 0.2 u_2 \end{pmatrix} \begin{pmatrix} p_1 \\ p_2 \end{pmatrix} \right]\end{split}\]