transfer function

The transfer function of a linear dynamical system is the ratio of the Laplace transformMathworldPlanetmath of its output to the Laplace transform of its input. In systems theory, the Laplace transform is called the “frequency domain” representation of the system.

Consider a canonical dynamical systemMathworldPlanetmathPlanetmath

x˙(t) = Ax(t)+Bu(t)
y(t) = Cx(t)+Du(t)

with input u:RRn, output y:RRm and state x:RRp, and (A,B,C,D) are constant matrices of conformable sizes.

The frequency domain representation is


and thus the transfer function matrix is D+C(sI-A)-1B.

In the case of single-input-single-output systems (m=n=1), the transfer function is commonly expressed as a rational function of s:


The values zi are called the zeros of H(s), and the values pi are called the poles. If any of the poles has positive real part, then the transfer function is termed unstable; if all of the poles have strictly negative real part, it is stable.

Title transfer function
Canonical name TransferFunction
Date of creation 2013-03-22 14:02:41
Last modified on 2013-03-22 14:02:41
Owner lha (3057)
Last modified by lha (3057)
Numerical id 13
Author lha (3057)
Entry type Definition
Classification msc 93A10
Defines frequency domain
Defines stable
Defines unstable