Usually, for minimum phase systems, if a controller makes the output error to be zero (for a bounded reference signal), the states are also bounded.

However, this is not true in NMP (Non Minimum Phase) systems.

It is possible that for an NMP system, the feedback controller makes the output track its reference signal perfectly, but the system states are unstable. The instability of the system is not reflected in the output, which is the danger.

The response of a non minimum phase system to a step input has an "undershoot". This means, if the output was initially zero and the steady state output is positive, the output becomes first negative before changing direction and converging to its positive steady state value. Intuitively, you see why this is annoying from a controller point of view. Imagine you take action to change the temperature of the water in your shower because it is too cold. However, before becoming warmer, the water becomes even colder. You may think in the first moment, you turned the knob in the wrong direction, so you turn it back. Well, this would be a wrong decision because this will make the water even colder in the long run. You may have noticed that this example is actually quite realistic in most shower systems.

Generally, however, we avoid poles in the RHP. In regard to zeroes, the amplitude response of a RHP zero at s=p is identical to that of a LHP zero at s=-p. The difference is in the phase response. The phases are of opposite signs, with the phase for the RHP equal to pi radians plus the phase for the LHP. Due to this difference, we have come to call designs or systems whose poles and zeroes are restricted to the LPH minimum phase systems.