Performance limitation in the tracking and regulation problem for discrete-time systems

In this paper, the optimal tracking performance of discrete-time, multi-input multi-output, linear-time invariant systems is investigated, in which there exist a stochastic disturbance signal in feed-forward channel, and and the output feedback is subject to an additive white Gaussian noise corruption. The problem under consideration amounts to determine the minimal error in tracking a Brownian motion subject to the channel power constraint. An lower bound of the minimal tracking error is attainable by searching through all stabilizing two-parameter controllers. It is shown that tracking performance is closely dependent on non-minimum phase zeros, unstable poles and demonstrated how the disturbance and noise may degenerate the tracking performance. Finally, an example is given to illustrate the analytical result obtained.