The two main problems with variable-structure control are control input chattering and the assumption of known parameter uncertainty bounds, the second of which is studied. The robustness of a recently proposed variable-structure control approach with estimated bounds algorithm 1 in the paper is first examined Stability analysis of the proposed variable-structure adaptive control schemes is establislied in the Lyapunov sense. To improve robustness of algorithm 1, four new algorithms are proposed and a comparative study of these is presented. Algorithm 1 performs well without the other uncertainty disturbances except parameter uncertainty. However, it may lead to an unstable system if input disturbances exist. Algorithm 2 requires the upper bounds of the uncertainty parameters. Algorithm 3 has a good performance on robustness to input disturbances besides parameter uncertainty. However, the tracking errors of algorithm 3 do not converge to zero even without input disturbances. To improve this, two modifications of algorithm 3 are proposed. Algorithm 4 has good tracking performance and robustness but requires knowledge of the parameter uncertainty bounds. Algorithm 5 gives better tracking performance and using the same kinds of previous knowledge as in algorithms 1 and 3. Robustness of the proposed algorithms to input disturbances is investigated. Extensive comparative simulation results are presented to support the theoretical analysis of the paper.