it is known that the stability of a system with negative feedback may be analized through the Nyquist stability criterion, which is based on observing the number of turns around the point (-1;0) in the complex plane.

But, what if we want to apply the same criterion for a positive feedback system? Is it correct or should be modified in some ways?

Can we say also for positive feedback that the system is unstable if and only if there are at least 1 pole with positive real part?


1 Answer 1


You could just multiply $H$ with minus one, change the positive feedback to negative feedback and proceed with the standard analysis for the Nyquist stability criterion. Here $H$ is the transfer function in the feedback path as shown in this image.

  • $\begingroup$ But if I do this operation, the open loop transfer function keeps the same as before, and so the Nyquist plot. How does the sign of H affect the Nyquist plot? $\endgroup$
    – Kinka-Byo
    Jan 22, 2020 at 7:03
  • $\begingroup$ @Kinka-Byo For the Nyquist stability criterion you need to use $L(s)=G(s)\,H(s)$. $\endgroup$
    – fibonatic
    Jan 22, 2020 at 9:50

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