  Approximate simulation, an extension of simulation relations from formal
methods to continuous systems, is a powerful tool for hierarchical control of
complex systems. Finding an approximate simulation relation between the full
"concrete" system and a simplified "abstract" system establishes a bound on the
output error between the two systems, allowing one to design a controller for
the abstract system while formally certifying performance on the concrete
system. However, many real-world control systems are subject to external
disturbances, which are not accounted for in the standard approximate
simulation framework. We present a notion of robust approximate simulation,
which considers external disturbances to the concrete system. We derive output
error bounds for the case of linear systems subject to two types of additive
disturbances: bounded disturbances and a sequence of (unbounded) impulse
disturbances. We demonstrate the need for robust approximate simulation and the
effectiveness of our proposed approach with a simulated robot motion planning
example.
