0
$\begingroup$

I am reading the textbook "Modern Control Engineering" by Katsuhiko Ogata. There is a section on deriving the transfer function from the state space equations dx/dt = Ax + Bu and y = Cx + Du

After taking Laplace Transforms and some simplification, we get G(s) = C(sI - A)^-1 B + D which is fine.

How this then turns into G(s) = Q(s) / |sI - A| stumps me. Here, Q(s) is a polynomial in s.

Can anyone help out?

$\endgroup$
2
  • 2
    $\begingroup$ Start by showing what you have tried - someone may then point out an error or something. $\endgroup$
    – Solar Mike
    Commented Oct 6, 2023 at 14:03
  • $\begingroup$ What is the expression for $Q(s)$? Expressing the inverse of a matrix (in this case $(sI-A)$) usually involves the determinant of the same matrix (in this case $|sI-A|$). $\endgroup$
    – AJN
    Commented Oct 6, 2023 at 17:48

1 Answer 1

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.