Identification of multivariable Hammerstein systems using rational orthonormal bases

A non-iterative algorithm for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein systems is presented. The proposed algorithm is numerically robust, since it is based only on least squares estimation and singular value decomposition. Under weak assumptions on the persistency of excitation of the inputs, the algorithm provides consistent estimates even in the presence of coloured noise. Key in the derivation of the results is the use of rational orthonormal bases for the representation of the linear part of the system. An additional advantage of this is the possibility of incorporating prior information about the system in a typically black-box identification scheme.