Fully Parametrized State-Space Models in System Identification

In this paper we consider identification of multivariable linear systems using state-space models. A new model structure which is fully parametrized is introduced. All systems of a given order can be described with this model structure and thus relieve us from all the internal structural issues otherwise inherent in the multivariable state-space identification problem. We present an identification algorithm which minimize a regularized prediction error criterion. We show that the proposed model structure retains the statistical properties of the standard identifiable model structures. The proposed identification algorithm is shown to locally converge to the set of true systems. Examples are given illustrating the results as well as showing the practical use of the proposed model structure using real data