Briefly describe the Nyquist stability criterion in control theory.

• A. The open-loop transfer function L(s) around the -1 point; count encirclements relative to the number of right-half-plane poles.
• B. The poles of the closed-loop system only.
• C. The zeros of the numerator of the closed-loop transfer function.
• D. The time-domain step response.

Answer: (A)

Nyquist stability looks at how the open‑loop transfer function behaves when s runs along the imaginary axis and around infinity, and it uses the -1 point in the complex plane as a critical reference. You plot L(jω) and count how many times the plot winds around the point -1. This encirclement count, together with how many open-loop poles lie in the right half of the complex plane, tells you how many closed-loop poles end up in the right half-plane. The standard relation is that the encirclement count around -1 equals the number of unstable closed-loop poles minus the number of unstable open-loop poles. For a typical case with no unstable open-loop poles, stability requires zero encirclements of -1. So the plan is to examine L(s) around the -1 point and count encirclements, in relation to the right-half-plane poles.