Nyquist Stability Criterion

Nyquist Stability Criterion is a graphical method used in control-system analysis to determine the closed-loop stability of a feedback system by examining how the frequency response of the open-loop transfer function $G(s)H(s)$ encircles the critical point $(-1,\,0)$ in the complex plane.It is based on the Nyquist plot and relates the number of encirclements of the critical point to the number of open-loop poles in the right-half of the $s$-plane, allowing engineers to determine whether the closed-loop system is stable and to assess gain margin, phase margin, and relative stability without directly solving the closed-loop characteristic equation.