MATH319 Slides

54 The transfer function of (A,B,C,D) (see also 92)

Definition (Transfer function)

The transfer function of (A,B,C,D) is

T(s)=D+C(sI-A)-1B.

Lemma

If sI-A is invertible, then the following block matrices are row equivalent over 𝐂(s):

[A-sIBCD][-I(sI-A)-1B0T(s)].

We observe that T(s) can be computed exactly by matrix multiplication and elementary row operations. The next results tell us about T(s).