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⁢(s⁢I-A)-1⁢B. In particular, with A,B,C as in frame 57 and D∈𝐂,

T⁢(s)=det⁡[s⁢I-AB-CD]det⁡[s⁢I-A].

Beware the minus signs!