A design criterion is developed to achieve the robust stabilization of a feedback system with time-varying non-linear uncertainties. Moreover, an effective design algorithm is derived to achieve the robust optimization of a feedback system subjected to time-varying non-linear uncertainties. The theory of minimumH∞-norm and the optimal interpolation technique are employed to solve this robust optimization problem. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or is non-minimum phase. From the result of the robust optimization, we can predict the maximum sector bound of non-linear uncertainties that can be tolerated in the feedback system.