This paper studies the tracking performance of the single-input single-output (SISO), finite dimensional, linear and time-invariant (LTI) system over an additive white Gaussian noise (AWGN) channel with finite control energy and channel input energy constraint. A new performance index is proposed which is minimized over all stabilizing two-degree-of-freedom controllers. The explicit expressions of the lower bound of the tracking performance and the minimum of signal-to-noise required are obtained. The results show that the lower bound is correlated to the unstable pole, nonminimum phase zero and the channel scaling factor. Finally, one example is given to validate the conclusions by adopting the special inner-outer factorization.
