Cases

Cases are like if/else statements for variables. Let

a(t)={x1c1x2c2⋮xncna(t)=\begin{cases}x_1\quad c_1\\ x_2\quad c_2\\\quad\vdots \\x_n\quad c_n\end{cases}

This means a(t)=x1a(t)=x_1 if condition c1c_1 is true a(t)=x2a(t)=x_2 if condition c2c_2 is true so on...

a(t)=xns.t.cn is truea(t)=x_n\quad \text{s.t.}\quad c_n\text{ is true}

Also cic_i cannot be true whenever cj∀j∈{1,...,n},j≠ic_j\quad\forall \quad j\in \{1,...,n\},j\neq i