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The advantage of IIR filters over FIR ones is that the former require a much lower order to obtain the desired response specifications. However, the existing deterministic techniques for IIR filter bank design based on heuristic usually lead to too high order IIR filters and thus cannot be practically used. In this paper, we propose new method to solve the low-order IIR filter bank design, which is based on linear matrix inequalities (LMI) optimization. Our focus is the QMF bank design, although other IIR filter related problems can be treated and solved in similar way.