The paper develops a technique for the robust and stable design of digital infinite impulse response (IIR) filters. As the error surface of IIR filters is generally multi-modal, global optimization techniques are required to design efficient digital IIR filter in order to avoid local minima. In this paper a real-coded genetic algorithm (RCGA) with arithmetic-average-bound-blend crossover and wavelet mutation is applied to design the digital IIR filter. A multicriterion optimization is employed as the design criterion to obtain the optimal stable IIR filter that satisfies the different performance requirements like minimizing the Lp-norm approximation error and minimizing the ripple magnitude. The proposed real-coded genetic algorithm is effectively applied to solve the multicriterion, multiparameter optimization problems of low-pass, high-pass, band-pass, and band-stop digital filters design. The computational experiments show that the proposed method is superior or atleast comparable to other algorithms and can be efficiently used for higher order filter design.