  Control systems should enforce a desired property for both expected modeled
situations as well as unexpected unmodeled environmental situations. Existing
methods focus on designing controllers to enforce the desired property only
when the environment behaves as expected. However, these methods lack
discussion on how the system behaves when the environment is perturbed. In this
paper, we propose an approach for analyzing control systems with respect to
their tolerance against environmental perturbations. A control system tolerates
certain environmental perturbations when it remains capable of guaranteeing the
desired property despite the perturbations. Each controller inherently has a
level of tolerance against environmental perturbations. We formally define this
notion of tolerance and describe a general technique to compute it, for any
given regular property. We also present a more efficient method to compute
tolerance with respect to invariance properties. Moreover, we introduce a new
controller synthesis problem based on our notion of tolerance. We demonstrate
the application of our framework on an autonomous surveillance example.
