**Last but one tutorial from the series about the Control Systems topic written by Nasir, our active member of the community. Will this definition help you?**

#### Introduction

In Analyzing and designing of any system, the most important factor is the mathematical modeling of that system. There are many mathematical models to describe control systems.

In physics, transfer function maybe defined as mathematical representation (in terms of frequency) of interrelation between input and output in linear time uninterrupted systems with zero pint equilibrium and zero initial conditions. If talking particularly about control systems then it can be defined as the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all zero initial conditions.

Transfer function is function of complex variables. The transfer function can be obtained by simple algebraic jugglery of differential equations that illustrates the system. Transfer function can represent higher order systems also, even infinite dimensionless systems which regulates on partial differential equations.