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

MATLABproofrelationship

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.

Best Answer

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: http://en.wikipedia.org/wiki/Determinant#Useful_identities.
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