Most control system analysis and design techniques are based on linear systems theory. Although we could develop these procedures using the state space models, it is generally easier to work with transfer functions. Basically, transfer functions allow us to make algebraic manipulations rather than working directly with linear differential equations (state space models). To create transfer functions, we need the notion of the Laplace transform.
The Laplace transform of a time-domain function, f(t), is represented by L[f(t)] and is defined as
The Laplace transform is a linear operation, so the ...