A Subspace Based Instrumental Variable Method for State-Space System Identification

Abstract

Traditional prediction-error techniques for multivariable system identification require canonical descriptions using a large number of parameters. This problem may be avoided using subspace based methods, since these estimate a state-space model directly from the data. In this paper, a subspace based technique for identifying general finite-dimensional linear systems is presented and analyzed. Similar to subspace based identification schemes, the space spanned by the extended observability matrix is first estimated. The system parameters are then extracted by reparametrizing the nullspace of the subspace estimate in terms of the coefficients of the characteristic polynomial. A quadratic problem is obtain and based on a statistical analysis, an optimal weighting derived.