System Identification using Overparameterized State-Space Models

In this report we consider identication of linear timeinvariant nite dimensional systems using statespace models We introduce a new model structure which is fully parametrized ie all matrices are filled 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 identication problem The models are obtained with an identication 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 tiable model structures We prove under some mild assumptions that the proposed identication 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