The robust control design problem is studied for a class of uncertain dynamical systems. The uncertainty of the system is time varying. The only assumption on the uncertainty is that it is bounded. No statistical property of the uncertainty is ever assumed and utilized. The robust control does not need thea prioriestimation on the bound of uncertainty. An adaptive algorithm for the on-line estimation of the bound is constructed and the robust control is only dependent on this estimation. The adaptive algorithm is a modification of previous work by Corless and Leitmann (1983). The advantages of this new algorithm include a constant control design parameter (which should have been time varying previously) and the applicability to linear systems with mismatched uncertainty and measurement noise.