In the context of Nyquist stability, what does an encirclement of the point -1 in the complex plane indicate?

• A. Encirclements are irrelevant to stability.
• B. Encirclements indicate phase margin only.
• C. Encirclements can indicate potential instability depending on open-loop poles.
• D. Encirclements guarantee stability.

Answer: (C)

Nyquist stability uses how the open-loop transfer function L(jω) maps the imaginary axis into the complex plane, and specifically how many times and in what sense this plot winds around the critical point -1. That point corresponds to the closed-loop characteristic equation 1 + L(s) = 0, so encirclements of -1 reflect conditions where the closed-loop system could have poles in the right half of the s-plane.

What matters is how many open-loop poles lie in the right half-plane. If there are no open-loop right-half-plane poles, then encircling -1 indicates the presence of right-half-plane zeros of 1 + L(s), i.e., unstable closed-loop poles. If there are right-half-plane poles in the open-loop transfer function, encirclements can still be consistent with a stable closed loop if the number of encirclements matches the pole count in just the right half-plane; the balance P − Z determines stability.

So encirclements can indicate potential instability, but only in the context of how many open-loop poles lie in the right half-plane. Without that information, encirclements by themselves do not guarantee stability or instability.