  In this paper, we study the control properties of a new class of stochastic
ensemble systems that consists of families of random variables. These random
variables provide an increasingly good approximation of an unknown discrete,
linear-time invariant (DLTI) system, and can be obtained by a standard,
data-driven procedure. Our first result relates the reachability properties of
the stochastic ensemble system with that of the limiting DLTI system. We then
provide a method to combine the control inputs obtained from the stochastic
ensemble systems to compute a control input for the DLTI system. Later, we deal
with a particular kind of stochastic ensemble system generated from realizing
Bernoulli random variables. For this, we characterize the variance of the
computed state and control. We also do the same for a situation where the data
is updated sequentially in a streaming fashion. We illustrate the results
numerically in various simulation examples.
