Which summary captures the core criterion for feedback stability in control systems?

• A. Stable systems have all poles in the left half-plane; root locus shows how poles move with gain; ensure margins so closed-loop remains stable (gain/phase margins).
• B. Stability depends only on circuit temperature.
• C. If the closed-loop has a fast response, it is always stable.
• D. Stability is determined only by the open-loop gain, not by pole placement.

Answer: (A)

In continuous-time feedback systems, stability means all closed-loop poles lie in the left half of the s-plane so the response decays over time. The closed-loop poles are determined by the characteristic equation 1 + L(s) = 0, where L(s) is the open-loop transfer function (gain times plant). As you change the loop gain, the root locus shows how those poles move in the complex plane. If any pole crosses into the right half-plane, the system becomes unstable, so you want the locus to stay in the left half-plane for the gains you plan to use. Gain margin and phase margin quantify how much you can perturb the gain or loop phase before crossing into instability, giving a practical measure of robustness.

Other statements miss the essential idea: temperature can affect component values but does not define stability on its own; a system can be fast yet unstable if its poles are improperly placed; and stability depends on the feedback loop as a whole, not merely on open-loop gain or on how fast the response is.