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Computing Largest Tolerable Disturbance Sets

For systems with disturbances, the robustness of a state constraint can be characterized by finding the largest set of disturbances such that the constraint is always satisfied. We call this the largest tolerable disturbance set. This paper presents a numerical sampling-based algorithm that iteratively computes upper and lower bounds on the largest tolerable disturbance set. This algorithm mainly applies to Lipschitz continuous nonlinear systems with inputs that enter the system linearly and with polytope state constraint sets. We prove that our algorithm finds upper and lower bounds that monotonically converge (in the Hausdorff sense) to the largest tolerable disturbance set.