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Abstract
Switching properties of the time-optimal control are obtained for a linear time-invariant system for which the state matrix has all its eigenvalues real, the control u satisfies the constraint |u| ≤ 1 and the state vector x the constraint |a´x| ≤ K, a being a constant vector associated with an eigenspace of A. These switching properties are extensions of the property that, when no state constraints are present, u has at most n − 1 switches between the values + 1 and − 1.