An evolutionary synthesis method to design low-sensitivity IIR filters with linear phase in the passband is presented. The method uses a chromosome coding scheme based on the graph adjacency matrix. It is shown that the proposed chromosome representation enables to easily verify invalid individuals during the evolutionary process. The efficiency of the proposed algorithm is tested in the synthesis of a fourth-order linear phase elliptic lowpass digital filter. Categories and Subject Descriptors: I.0 General General Terms: Algorithms, Design