Transfer functions

In this chapter, we use the Laplace transform to introduce one of the most ubiquitous types of mathematical dynamic system representation: the transfer function. The transfer function joins the state-space model and the I/O ODE mathematical representations of dynamic systems, the third of our four mathematical representations. The fourth, the frequency response function, is closely related to the transfer function and is introduced in chapter 13.

As we will see in section 11.1, the transfer function is closely related to the I/O ODE. The transfer function encodes the same information as the I/O ODE, but in a form that highlights the system’s frequency response and the relation between an input and an output.