A Nyquist plot of the system does not encircle the point -1+j0, and there are no poles of the openloop transfer function in the right half of the s-plane. What can be concluded about the stability of the system?

Correct option is A

​$$\text{Using the Nyquist stability criterion:} \\[6pt]Z = P + N \\[8pt]\text{where} \\[4pt]\bullet \ P = \text{ number of open-loop poles in the Right Half Plane (RHP)} \\[2pt]\bullet \ N = \text{ number of encirclements of the point } -1 + j0 \\[2pt]\bullet \ Z = \text{ number of closed-loop poles in the RHP} \\[8pt]\text{Given in the question:} \\[6pt]\bullet \ \text{No encirclement of } -1 + j0 \Rightarrow N = 0 \\[2pt]\bullet \ \text{No open-loop poles in the RHP } \Rightarrow P = 0 \\[8pt]\text{Therefore:} \\[6pt]Z = 0 + 0 = 0 \\[8pt]\text{This means there are no closed-loop poles in the RHP, so the closed-loop system is stable.}$$​​