Control engineering[edit]
In control engineering and control theory the transfer function is derived using the Laplace transform.
The transfer function was the primary tool used in classical control engineering. However, it has proven to be unwieldy for the analysis of multiple-input multiple-output (MIMO) systems, and has been largely supplanted by state space representations for such systems.[citation needed] In spite of this, a transfer matrix can be always obtained for any linear system, in order to analyze its dynamics and other properties: each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.
A useful representation bridging state space and transfer function methods was proposed by Howard H. Rosenbrock and it is referred to as Rosenbrock system matrix.