\documentclass[]{article}

\begin{document}


Circuito Boost, parametrizado:

\begin{eqnarray}
\dot{z}_{1}&=&- \mu z_{2} +1 \nonumber \\
\dot{z}_{2}&=& \; \; \mu z_{1} - z_{2} / Q \nonumber \\
y&=& z_{2}
\end{eqnarray}


Salida plana y sus derivadas:
\begin{eqnarray}
F&=&{\frac{1}{2}} \left( z_{1}^2+z_{2}^2 \right) \nonumber \\
\dot{F}&=& z_{1} \; \left(- \mu z_{2} +1 \right)
+ z_{2} \left( \mu z_{1} - z_{2} / Q \right)= z_{1} - z_{2}^{2} / Q  \nonumber \\
\ddot{F}&=& - \mu z_{2} +1 - 2 {\frac{z_{2}}{Q}} \left( \mu z_{1} - z_{2} / Q \right) \nonumber \\
%-\mu \left( \mu z_{1} - z_{2} / Q \right)
%+ \mu \left( - \mu z_{2} +1  \right) -  \left( \mu z_{1} - z_{2} / Q \right) / Q 
&=& - \mu z_{2} +1 - 2 {\frac{z_{2}}{Q}}
\left( \mu {\frac{1}{\mu}}\left(\dot{z}_{2}+z_{2} / Q \right) - z_{2} / Q \right) \nonumber \\
&=&- \mu z_{2} +1 - 2 {\frac{z_{2}}{Q}}  \dot{z}_{2} 
\end{eqnarray}


\end{document}
