form of a condition function using leftbrace

In fact I want to write this function definition with the leftbrace :

And here is the code that I have written:

\begin{aligned} Si \,\,\,\,\,\, \varepsilon Q_s \geq \Delta Q_s\\ Si \,\,\,\,\,\, \varepsilon Q_s \leq -\Delta Q_s\\ Si \,\,\,\,\,\, \varepsilon P_s \geq \Delta P_s\\ Si \,\,\,\,\,\, -\Delta P_s \leq \varepsilon P_s \leq \Delta P_s\\ Si \,\,\,\,\,\, \varepsilon P_s \leq -\Delta P_s \end{aligned}


It can be done with cases and alignedat. Since you seem to write in French, I took the liberty to use the French inequality signs. I propose also a second alignment which looks lighter, in my opinion: \documentclass[9pt]{extbook}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}

\usepackage{array}
\usepackage{amsfonts,amssymb}
\usepackage{empheq}

\usepackage[francais]{babel}
\def\fgeq{\geqslant}
\def\fleq{\geqslant}

\begin{document}

\begin{cases} \begin{alignedat}{3} &\text{Si} & \enspace & \varepsilon Q_s \fgeq \Delta Q_s & \quad\implies & H_Q = 1\\ & \text{Si} & & \varepsilon Q_s \fleq -\Delta Q_s & \implies & H_Q = -1\\ & \text{Si} & & \varepsilon P_s \fgeq \Delta P_s & \implies & H_P = 1\\ & \text{Si} & & -\Delta P_s \fleq \varepsilon P_s \fleq \Delta P_s & \implies & H_P = 0\\ & \text{Si} & & \varepsilon P_s \fleq -\Delta P_s & \implies & H_P = -1 \end{alignedat} \end{cases}

\end{document}


A single cases environment (provided by the amsmath package) is all you need:

\documentclass{article}
\usepackage{amsmath} % for 'cases' environment
\begin{document}

$$\begin{cases} \text{Si } \varepsilon Q_s \geq \Delta Q_s & \Rightarrow H_Q=\phantom{-}1 \\ \text{Si } \varepsilon Q_s \leq -\Delta Q_s & \Rightarrow H_Q=-1 \\ \text{Si } \varepsilon P_s \geq \Delta P_s & \Rightarrow H_P=\phantom{-}1 \\ \text{Si }{-}\Delta P_s\leq\varepsilon P_s\leq\Delta P_s & \Rightarrow H_P=\phantom{-}0\\ \text{Si } \varepsilon P_s \leq -\Delta P_s & \Rightarrow H_P=-1 \end{cases}$$

\end{document}