I was given the system defined by the open-loop transfer function:
I was told to use the Nyquist criterion to determine stability. Examining the Nyquist plot shows one CCW encirclement of the (-1,0) point. The open-loop system has two RHP poles (although they are repeated poles). Using the equation:
Where N=-1 and P=2, we see Z=1. This means there should be 1 RHP pole in the closed-loop transfer function and we would expect the system to be unstable. However, upon inspection of the impulse response, and step response the system does in fact appear stable. I'm struggling to understand why this system is not unstable. My initial thought is that the repeated pole at s=1 should only be counted once, but I haven't been able to find any literature to suggest this.