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This paper develops procedures based on H∞ techniques to achieve position control underactuated manipulators. First, in a deterministic approach, we compare two nonlinear H∞ control techniques in order to verify the differences in structure and robustness of controllers based on quasi-linear parameter varying (LPV) representation and game theory. In this case, the use of brakes is necessary when a fault occurs. Secondly, we develop a procedure based on Markov theory, where an H∞ Markovian controller is used to control the position of manipulators subject to abrupt changes in configuration. In this case, the brakes are not necessary to guarantee the stability of the system. The theory developed is tested in an actual manipulator setup.