On the choice of noise models and their bounds in set-membership identification

Different noise models and the corresponding membership sets are studied in this paper. In particular, under some conditions on the noise sequences, we show that: (1) if the noise bound is unknown and tight, then the size of the membership sets converges to zero asymptotically and (2) if the noise bound is unknown but tight, then the estimated noise bound calculated from the observed input-output data converges to the true but unknown noise bound asymptotically