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Rigid-body attitude control is motivated by aerospace applications that involve attitude maneuvers or attitude stabilization. The set of attitudes of a rigid body is the set of 3 X 3 orthogonal matrices whose determinant is one. This set is the configuration space of rigid-body attitude motion; however, this configuration space is not Euclidean. Since the set of attitudes is not a Euclidean space, attitude control is typically studied using various attitude parameterizations. Motivated by the desire to represent attitude both globally and uniquely in the analysis of rigid-body rotational motion, this article uses orthogonal matrices exclusively to represent attitude and to develop results on rigid-body attitude control. An advantage of using orthogonal matrices is that these control results, which include open-loop attitude control maneuvers and stabilization using continuous feedback control, do not require reinterpretation on the set of attitudes viewed as orthogonal matrices. The main objec tive of this article is to demonstrate how to characterize properties of attitude control systems for arbitrary attitude maneuvers without using attitude parameterizations.