Effect of RHP zeros on stability
To ensure that any feedback system is stable, the loop gain needs to have a phase difference less than 180 degrees when its magnitude is unity, in other words it needs to ave sufficient phase margin.
Having a right half plane zero is non-favorable in this sense. It increases your loop gain and increases your phase difference. Consequently, your phase margin is definitely going to reduce because of the RHP zero and hence your stability is degraded.