Identifying Positive Real Models in Subspace Identification by Using Regularization

This paper deals with the lack of positive realness of identified models that may be encountered in many stochastic subspace identification procedures. Lack of positive realness is an often neglected, but important problem. Subspace identification algorithms fail to return a valid linear model if the so-called covariance model, which is obtained from an intermediate realization step in the subspace identification algorithm, is not positive real. The main contribution of this paper is to introduce a regularization approach to impose positive realness on the covariance model. It is shown that positive realness can be imposed by adding a regularization term to a least squares cost function appearing in the subspace identification procedure.