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Quantitative design of robust control systems proposes a transparent and practical controller design methodology for uncertain plants. In the case of large plant uncertainties, the resulted robust controller would be unnecessarily high order with large bandwidth. On the other hand, adaptive controllers can also tackle the control of unknown uncertain plants. However, the controller would be nonlinear and time varying. In this paper, a combined design methodology based on quantitative feedback theory (QFT) and externally excited adaptive system (EEAS) is proposed. This controller can handle large plant parameter uncertainties with lower bandwidth. Also, a random optimization technique is employed to optimally design the overall robust adaptive controller. Simulation results are used to show the effectiveness of the proposed design methodology.