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The paper focuses on the attitude dynamics and control of satellites orbiting rotating asteroids. The general formulation of the satellite equations of motion in an equatorial eccentric orbit is obtained through Lagrangian method. The linearized system model is derived and the stability analysis is presented. The control laws for three-axis attitude control of satellites are developed and a closed-form solution of the system is derived. For an illustration of the linear analysis followed by the numerical simulation of the governing nonlinear equations of motion of the satellite, several asteroids (Eros, Castalia, Vesta, Ida, and Gaspra) are considered. Attitude resonances for satellites in retrograde orbits are found. The results of the linear system model compare well with the corresponding system nonlinear equations of motion. The proposed controllers are successful in stabilizing the attitude of the satellites even in presence of high attitude disturbances and orbital eccentricities.