Optimal tracking performance of discrete-time systems over an additive white noise channel

This paper studies the optimal tracking performance of multiple-input multiple-output (MIMO), finite dimensional, linear time-invariant discrete-time systems with a power-constrained additive white noise (AWN) channel in the feedback path. We adopt the tracking error power as a measure of the performance and examine the best achievable performance by all two-parameter stabilizing controllers. In the due process, a scaling scheme is introduced as a means of integrating controller and channel design, and is optimized to better the tracking performance. In contrast to the standard setting where tracking of a step reference signal is conducted with no communication constraint, in which the tracking error can be made as zero for minimum phase plants, it is shown explicitly herein that the tracking performance will be additionally constrained by the plant unstable poles, as a consequence of noisy, power-constrained channels in the feedback loop.