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An optimal design method for stable IIR (Infinite Impulse Response) filters under the min-max criterion is proposed. The design problem considered is the complex Chebyshev approximation of a rational function including the stability constraint. We formulate this problem as a problem of real linear semi-infinite programming problem using the real rotation theorem. The problem is solved by the three-phase method; one of the methods is used for solving semi-infinite programming problems. The three-phase method includes three operations. In the first operation, some active constraint candidates are selected by the iterative simplex method. Next, the second operation integrates some degenerate constraints. In the third operation, the approximate solution obtained up to the second operation is adjusted so as to satisfy the optimality condition. The filters designed by the method are found to be more precise than those designed by the conventional method. Several design examples are presented to demonstrate the effectiveness of the proposed method. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(6): 17-23, 2011; Published online in Wiley Online Library (). DOI 10.1002/ecj.10330 [ABSTRACT FROM AUTHOR]