Question on Matlab's ss2tf function

Hello, Looking at the function ss2tf - which converts state space to transfer function I am trying to understand how the numerator polynomial is calculated. I understand how the denominator polynomial is calculated, but can't figure out how the numerator works out.

The numerator is calculated by: num = det(sI- A +BC) -det(sI-A)

note: A, B, C, D are the regular state space matrices (in this case D=0). So the numerator comes from the eigenvalues of the matrix A-BC and the matrix A

I would be grateful for hints in the derivation or a pointer to a paper.

Thanks. David

Reply to
Dave
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It is all there in the Matlab code. Just

type ss2tf

and you'll see how.

--Nasser

Reply to
Nasser Abbasi

Looking at the ss2tf function was how I got the above function for the numerator. My question is how is it derived. Normally the transfer function is given as C inv(sI-A)B +D. Substituting the adjoint and determinant for the inverse allows you to determine the denominator polynomial. So how do you go from the above formula to the numerator polynomial?

Cheers, Dave

Reply to
Dave

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