Estimation of Linear Parameter-Varying affine state space models using synchronized periodic input and scheduling signals

During the past decades some very interesting results have been obtained in controller synthesis using Linear Parameter-Varying (LPV) systems. However, the LPV models are commonly required to be transformed into State Space (SS) form. We tackle the LPV SS identification problem directly in the frequency domain. To the best of our knowledge, this is a novel approach. When the input and scheduling are chosen to be periodic and synchronized, the state space equations are structured and sparse in the frequency domain. The parameters of these state space equations are estimated by minimizing a weighted non-linear least squares criterion. Starting values are generated via the Best Linear Time-Invariant (BLTI) approximation. The resulting model is also valid for non-periodic scheduling and input signals.