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Designing compensators with prespecified gain and phase properties has long been a trial-and-error exercise. Some recent efforts to optimize the filter-design process have generated a least-squares fit to some desired filter function. A new technique is presented which optimizes the design process in the L2 sense subject to performance inequality (feasibility) constraints. The achieved filter is shown to be locally optimal as well as feasible. In addition, the developed algorithm can be used to seek a minimal-order optimal filter.