Tracking under additive white Gaussian noise effect

This study investigates the tracking performance of continuous-time, multi-input multi-output, linear time-invariant systems in which the output feedback is subject to an additive white Gaussian noise corruption. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. The authors consider both the unity feedback and two-parameter control structure. In the former case, they derive an explicit bound, and in the latter an exact expression of the minimal tracking error attainable under the noise effect. Both results demonstrate how the additive white Gaussian noise may degenerate the tracking performance, and how the noise effect may intertwine with unstable poles and non-minimum phase zeros which are intrinsic characteristics of the plant.