System Identiication Using Overparametrized State-space Models

In this report we consider identiication of linear time-invariant-nite dimensional systems using state-space models. We introduce a new model structure which is fully parametrized, i.e. all matrices are lled with parameters. All multivariable systems of a given order can be described within this model structure and thus relieve us from all the internal structural issues otherwise inherent in the multivariable state space identiication problem. The models are obtained with an identiication algorithm by minimizing a regularized prediction error criterion. Some analysis is pursued which shows that the proposed model structure retains the statistical properties of the standard iden-tiiable model structures. We prove, under some mild assumptions, that the proposed identiication algorithm locally converges to the set of true systems. Inclusion of an additional step in the algorithm gives convergence to a balanced realization of the true system. Some results on the analysis of the sensitivity of the transfer function with respect to the parameters for a given realization are reviewed, which show that balanced realizations have low sensitivity. We show that for one particular choice of regularization the obtained model is in a norm minimal realization. Examples are given showing the properties of the proposed model structure using both real and simulated data.