  This paper considers discrete-time linear systems with bounded additive
disturbances, and studies the convergence properties of the backward reachable
sets of robust controlled invariant sets (RCIS). Under a simple condition, we
prove that the backward reachable sets of an RCIS are guaranteed to converge to
the maximal RCIS in Hausdorff distance, with an exponential convergence rate.
When all sets are represented by polytopes, this condition can be checked
numerically via a linear program. We discuss how the developed condition
generalizes the existing conditions in the literature for (controlled)
invariant sets of systems without disturbances (or without control inputs).
