  Suppose we can choose from a set of linear autonomous systems with bounded
process noise, the dynamics of each system are unknown, and we would like to
design a stabilizing policy. The underlying question is how to estimate the
dynamics of each system given that measurements of each system will be
nonsequential. Though seemingly straightforward, existing proof techniques for
proving statistical consistency of system identification procedures fail when
measurements are nonsequential. Here, we prove that the set-membership
estimator is statistically consistent even when measurements are nonsequential.
We numerically illustrate its strong consistency.
