Limitations on the closed-loop transfer function due to right-half plane transmission zeros of the plant

Transmission zeros of multivariable systems have important properties: they block the transmission of certain signals; C+-zeros impose bounds on the achievable loop gain; C+-zeros are crucial in the design of tracking servos. We establish here a limitation that the plant transmission zeros impose on the achievable closed-loop transfer function of any stable feedback system; specifically, we prove that under reasonable assumptions, the closed right-half plane transmission zeros of the plant will remain as transmission zeros of the I/O map of any stable feedback system (here the plant output is the feedback-system output).