Convergence properties of the membership set in the presence of disturbance and parameter uncertainty

The size of the membership set is investigated in the presence of bounded disturbance and l/sub 2/ bounded parameter uncertainty. A tight upper bound of the diameter of the membership set is derived, which indicates that the diameter does not converge to zero in general. Another upper bound of the diameter is also derived in a stochastic setting, where the disturbance and the parameter uncertainty are assumed to take a value near the worst ones with nonzero probability. The bound clarifies that the diameter converges to zero with probability one as the number of samples tends to infinity.