Does a net encirclement of (-1,0) always imply instability on a Nyquist plot?

Sean Humbert, 19 Nov 02

Instability is assessed via the Nyquist criterion, which says

Z = P + N

where

Z = # of closed loop RHP poles

P = # of open loop RHP poles

N = # of CW encirclements of -1

Hence, if the open loop transfer function has a pole in the RHP, then P=1 and for stability, we need N=-1 (i.e. we need one CCW encirclement of -1). Therefore a net encirclement of -1 does not always imply instability.