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Most existing methods for satellite attitude control assume that full knowledge of satellite attitude is available by algebraic manipulation of at least two vector measurements from attitude sensors such as Sun, Earth-horizon, Earth-magnetic or star tracker sensors. Kalman filtering is usually used when only one vector measurement is available, however, asymptotic stability of nonlinear and uncertain dynamics of satellite is not guaranteed in this case. This technical note presents a coupled nonlinear estimator-controller for satellite attitude determination and control by using a 3-axis gyro and a single vector measurement for a fully actuated satellite. We assume that the moment-of-inertia matrix of satellite is unknown. Asymptotic convergence of the satellite attitude and angular velocity to their desired values is proven. Performance of the proposed controller is illustrated in a realistic case study by simulation where a magnetometer is used to provide the single vector measurement.