The use of IIR filters instead of FIR filters in active noise and vibration control applications has some special advantages. However, multimodal error surface and instability problem of adaptive IIR filters has prevented its extensive use like FIR filters, and hence invokes more research on these subjects. In this paper, a new approach to design and stability analysis of adaptive IIR filters in active noise and vibration control applications, is proposed. The approach is based on transforming the ANVC problem to an output-error identification problem and the conditions for stability are derived using Popov hyperstabilty theory. The performance of the algorithm is compared to that of the Errikson's FuLMS and SHARF algorithms, and it is shown that the proposed algorithm has a faster convergence rate and the ability to converge to global optimum of filter weights.