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I am studying control syetems, and I have studied that the dominant poles of a system are the ones closer to the imaginary axis.

Now, consider a system with a pole at the origin. Can this pole at the origin be considered a dominant pole?

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You could get away with defining it as such (or extending the concept to the pole with the most positive real part).

But typically the concept of a dominant pole is applied to systems that are truly stable, and thus actually settle out. A system with singular poles on the imaginary axis (and no poles in the right-half plane) is considered "metastable", because with the right input it has a bounded response, but with the wrong input its response is unbounded.

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