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A linear autonomous control process is considered where the null control is an extreme point of the restraint set. In the event that = 0, 1 (hence, scalar control) necessary and sufficient conditions are given so that the reachable set from the origin (in phase space) contains the origin as an interior point. For vector-valued controls with each component in 0, 1, sufficient conditions are given so that the reachable set from the origin of a nonlinear autonomous control process contains the origin as an interior point.
Saperstone et al. (Sat,) studied this question.
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