Identification in the presence of bounded low-correlated noise

In this paper, we consider the problem of identification of discrete-time, single-input single-output linear time-invariant systems. The prior information about the unknown plant is that it belongs to a certain set of LTI systems. The plant can be identified using input-output experiments, where the input can be chosen freely and the observed output is corrupted by an additive disturbance which is assumed to be bounded and has low-correlation. This set of disturbance includes uniformly bounded sequences that satisfy a time averages correlation condition. The motivation for using such a disturbance set is that the disturbances resemble stochastic white noise processes. In particular, a white noise signal belongs to this set with high probability if the bound on the correlations approaches zero at a certain rate. This paper analyzes the problem of worst-case identification in the presence of the above set of disturbances.