In this paper a new robust adaptive IIR filter is designed for active noise and vibration control system. The developed adaptive algorithm has the capability to remain stable, when an upper bound of the uncertainties in the estimated model of the secondary path is known beforehand. It is proved that by using a nonlinear function of the measured error signal in the adaptation process the algorithm will exhibit a robustness property with respect to possible uncertainties in the secondary path model. This algorithm belongs to the class of RLS-type adaptive IIR filters in the modified filtered-x structure, and its stability is analyzed using Lyapanov theory.