Fundamental performance limitations of modulated and demodulated control systems

We consider feedback performance limitations for modulated and demodulated control systems whose base systems have non-minimum phase (NMP) zeros or unstable poles. We first derive a transfer function for the modulated system and then show how the poles and zeros of this function are related to those of the base system. We next analyse the behaviour of the poles and zeros, when the modulation frequency is varied. Bode and Poisson integral constraints for the modulated system are then considered. The effect of a base system delay is also discussed.