The problem of optimal trade-off-between robustness, in terms of time-delay margin, and performance of the ℒ 1 adaptive controller, is investigated in this paper. Although the architectures of the ℒ 1 adaptive control theory can be systematically tuned to trade-off performance for robustness, there is no methodology as of today for the design of the underlying filter towards obtaining the optimal performance. We present design schemes based on search for the design parameters or coefficients of the filter. We introduce filters of specific structures to satisfy the design specifications and investigate their properties over the space of the design parameters. We also borrow greedy randomized algorithms to analyze the system performance and robustness in the presence of uncertainties. In addition, we compute approximated sets of acceptable design parameters in both analytical and numerical ways. Illustrative examples show that these methods can achieve the desired control design specifications.