H∞ identification for nonlinear system based on generalized frequency response function

Based on the GFRF (generalized frequency response function), H_∞ identification for nonlinear system is investigated using the set membership identification theory. We applied the three-order truncated Volterra series to describe the nonlinear system, and accomplished the model identification by the Householder transformation that is a kind of orthogonal decomposition, and then derived the GFRF of the system. Moreover, by means of the set membership identification we give a measure of the model perturbation in a form well suited for H_∞-control methodologies. The effectiveness of the proposed procedure is tested on the numerical simulation.