The Size of the Membership Set in the Presence of Disturbance and Parameter Uncertainty

The size of the membership set is analyzed probabilistically in the presence of not only bounded disturbance but also l2bounded parameter uncertainty. Especially, the diameter of the membership set is estimated with a probabilistic confidence for a finite number of samples, where the regressor is assumed to be persistently exciting and the disturbance and the parameter uncertainty are assumed to be random variables. It is also shown that, under the same assumptions, the diameter converges to zero as the number of samples tends to infinity.