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?

  • 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

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