Poles of a State Space Model

In this section, we show that the *poles of a state-space model* are given
by the *eigenvalues* of the state-transition matrix .

Beginning again with the transfer function of the general state-space model,

Thus, *the eigenvalues of the state transition matrix are the
poles of the corresponding linear time-invariant system*. In
particular, note that the poles of the system do not depend on the
matrices , although these matrices, by placing system zeros,
can cause pole-zero cancellations (unobservable or uncontrollable
modes).

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