Accurate approximation of the largest null-controllable set for single-input bilinear systems

We present a method for the accurate approximation of the largest null-controllable set N_∞ for constrained bilinear systems. It is central to the presented approach that a simple quantitative measure of the accuracy of approximation can be determined. This measure can be used as a termination criterion for an iterative approximation of N_∞ with step sets. If the termination criterion is met, the proposed method results in an inner approximation of N_∞ that covers a requested percentage of N_∞.