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Tremor is a rhythmical and involuntary oscillatory movement of a body part and it is one of the most common movement disorders. Orthotic devices have been under investigation as a noninvasive tremor suppression alternative to medication or surgery. The challenge in musculoskeletal tremor suppression is estimating and attenuating the tremor motion without impeding the patient's intentional motion. In this research a robust tremor suppression algorithm was derived for patients with pathological tremor in the upper limbs. First the motion in the tremor frequency range is estimated using a high-pass filter. Then, by applying the backstepping method the appropriate amount of torque is calculated to drive the output of the estimator toward zero. This is equivalent to an estimation of the tremor torque. It is shown that the arm/orthotic device control system is stable and the algorithm is robust despite inherent uncertainties in the open-loop human arm joint model. A human arm joint simulator, capable of emulating tremorous motion of a human arm joint was used to evaluate the proposed suppression algorithm experimentally for two types of tremor, Parkinson and essential. Experimental results show 30-42 dB (97.5-99.2%) suppression of tremor with minimal effect on the intentional motion.