Tracking under additive white Gaussian noise effect

This paper 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. We consider both the unity feedback and two-parameter controllers. In the former case we 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 white Gaussian noise may impede the tracking performance, and how the noise effect may intertwine with such intrinsic characteristics of the plant as unstable poles and nonminimum phase zeros.