MATH319 Slides

65 A determinant formula for realization by SISO

Theorem

Let T(s) be a proper rational function. Then T(s) can be realised as the transfer function of a SISO (A,B,C,D), so T(s)=D+C(sI-A)-1B. In particular, with A,B,C as in frame 57 and D𝐂,

T(s)=det[sI-AB-CD]det[sI-A].

Beware the minus signs!