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Stability analysis of priority-based kinematic control algorithms for redundant robotic systems is approached in this paper. Starting from the classical applications in position control of manipulators, the kinematic-based approaches have lately been applied to, e.g., visual servoing and quadruped or multirobot coordination control. A common approach consists in the definition of several tasks properly combined in priority. In this paper, by resorting to a Lyapunov-based stability discussion for several prioritized inverse kinematics algorithms, sufficient conditions for the control gains and the tasks' design are given for the regulation problem. Two case studies show the practical implementation of the results.