Practice over 1000+ GATE-level questions from this topic!
Designed to match the latest GATE pattern with topic-wise precision, difficulty tagging, and detailed solutions.
The Nyquist plot of a strictly stable
having the numerator polynomial as
encircles the critical point -1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

The system stability cannot be ascertained.
The system is marginally stable.
The system is stable.
The system is unstable.
Given that open loop system
is stable.
No. of open -loop poles in RH of s-plane 
Also, No. of encirclements about critical point
is once,
Assume Nyquist Contour is clockwise
N = 1
N = P-Z
P= Open Loop Poles in RHP = 0
Z = Closed Loop Poles in RHP
Hence Z = -1 which is invalid
Now assume Nyquist Contour is Anti-Clockwise
N = -1 = P – Z
Hence Z = 1, which means one closed loop pole
lies in RHP and hence closed loop system is unstable
Option (d) is correct.