I have a transfer function in form of a matrix and want to determine the stability of the whole system. Now I'm wondering if I need to calculate the pole points or the eigenvalue. A friend of mine told me that the eigenvalues are equal to the pole points, but I guess this is not always true.
2026-03-28 05:21:55.1774675315
In what cases are the eigenvalue equal to the pole points?
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Eigenvalues are not always equal to poles. Due to the nature of the transfer function approach, only reachable and observable eigenvalues are visible in the polynomial roots. Because transfer function gives the relation between inputs and outputs, and does not interested in states.
Therefore, eigenvalues are equal to poles if and only if the system is reachable and observable.