Nonminimum Phase Zeros Effect on the Signal-to-Noise Ratio Channel Input Constraint in Continuous Time

It is well known that the presence of nonminimum phase (NMP) zeros increases already existing fundamental limitations. In this work we consider the minimal Signal-to-Noise Ratio (SNR) as the fundamental limitation in a control loop and, for an additive white Gaussian noise (AWGN) channel, propose a 2 degree of freedom (2DOF) controller to avoid the increase on the minimal SNR due to the presence of NMP zeros for a continuous time linear time invariant (LTI) plant model. We then characterize the presence of NMP zeros in the controller achieving the minimal SNR, when the plant model is minimum phase, but it is subject to a time delay. These controller NMP zeros then reveal that, if correctly placed to the same values, plant NMP zeros can result in a minimal SNR without the effect of NMP zeros, even in a 1 DOF controller strategy,