Identification of MIMO bilinear state space models using separable least squares

We present an algorithm to identify MIMO discrete-time bilinear state space models from input-output measurements. We estimate the system matrices by optimizing an output error criterion. This criterion depends linearly on some of the system matrices and nonlinearly on the others. Using the principle of separable least squares, we first solve for the matrices that enter nonlinearly and then obtain the others by solving a linear least squares problem. It is pointed out that subspace-based techniques can be used to estimate the order of the system and to compute initial estimates of the matrices that enter the criterion in a nonlinear way. The algorithm has been tested on a MIMO simulation example