What algorithm does SS2TF use in MATLAB 7.6 (R2008a)?

The documentation for SS2TF mentions the use of the following equation:

C*(s*I-A)^(-1)*B = [det(s*I-A+B*C) - det(S*I-A)] / det(S*I-A)

However, I cannot find any method to prove this equation.

Answer 1

[MathWorks Support Team]

To prove the relationship, you can substitute a dummy variable, say X, for sI-A and then rearrange the equation such that you obtain one in the form of Sylvester's determinant theorem:

det(X+a*b') = det(X)*(1+b'*X^(-1)*a)

This equation is the third and last equation in the "Useful identities" section of this URL:

https://en.wikipedia.org/wiki/Determinant

​​​​​#Useful_identities.