Identification of MIMO Hammerstein systems with non-linear feedback

Subspace identification algorithms are proposed in this paper for a class of multi-input multi-output (MIMO) discrete-time closed-loop Hammerstein systems. In particular, instrumental variable (IV) techniques are applied to solve the correlations between the input signals and the signals that are fed back into the system. An augmented IV identification approach is introduced to address a problem related to the application of the numerical efficient RQ decomposition algorithm to a rank-decreased correlation matrix. The contribution of this paper is to provide a unified approach to identify a class of non-linear closed-loop systems and solve the related numerical issues during the implementation. Analysis and numerical examples are presented to demonstrate the validity of the algorithms proposed in this paper.