Two or more systems connected in series. In Laplace transfer function form, two cascaded linear time-invariant systems with transfer functions $G_1\left(s\right)$ and $G_2\left(s\right)$ can be represented in block diagram form as

(a) Cascaded systems

where $X\left(s\right)$, $Y\left(s\right)$, and $Z\left(s\right)$, are the Laplace transforms of time signals $x\left(t\right)$, $y\left(t\right)$ and $z\left(t\right)$

Here, $Y\left(s\right)=G_1\left(s\right)X\left(s\right)$ and $Z\left(s\right)=G_2\left(s\right)Y\left(s\right)$,

so that $Z\left(s\right)=G_2\left(s\right)G_1\left(s\right)X\left(s\right)=\left[G_1\left(s\right)G_2\left(s\right)\right]X\left(s\right)$ and the cascaded processes can be replaced by a single equivalent system with transfer function $G_1\left(s\right)G_2\left(s\right)$

(b) Cascaded systems

Note that since $G_1\left(s\right)$ and $G_2\left(s\right)$ are simply algebraic functions of $s$, the order of multiplication is irrelevant.