Transfer Function

Transfer functions are a Laplace domain representation of the system. Commonly associated with the era of classical control theory.

Transfer Function

A transfer function is the Laplace transform of the impulse response of a linear, time-invariant system with a single input and single output when you set the initial conditions to zero. They allow us to connect several systems in series by performing convolution through simple multiplication.

From tutorial

The transfer function is the inverse of the characteristic polynomial. Hence the DE that has this transfer function $T(s)=\frac{1}{s^3+2s^2+3s}$ is

$y^{\prime \prime \prime }+2y^{\prime \prime }+3y=f(t)$

where $f(t)$ is the input of the system.

todo