For the state-feedback law

$$u=-Kx,$$

the closed-loop dynamics are governed by

$$A-BK.$$

The pole-placement problem chooses $K$ so the eigenvalues of $A-BK$ lie at desired locations.

Desired poles can be selected from stability and transient requirements. Moving poles farther into the stable region generally makes the associated modes decay faster, while complex-conjugate pole locations determine oscillation frequency and damping.

If the pair $(A,B)$ is controllable, arbitrary closed-loop pole placement is possible for the linear model.

Pole placement is therefore a model-based design method: first choose a desired closed-loop spectrum, then solve for a feedback gain that produces it.

It differs from optimal control, where the gain is chosen by minimizing a cost rather than by prescribing every pole directly.