On-and off-line identification of linear state space models

Abstract

A geometrically inspired matrix algorithm is derived for the identification of state space models for multivariable linear time-invariant systems and using possibly noisy input- output measurements data only. In this project, only a limited number of input and output data are required for the determination of the system matrices. The algorithm can be best described and also understood in the matrix formalism and consists in the following two steps. First step, a state vector sequence is realized as the intersection of the row spaces of two block Hankel matrices which is constructed by apply input - output data. Then, the system matrices are obtained at once from the least squares solution of a set of linear equations. When dealing with noisy data, this algorithm draws its excellent performance from repeated use of the numerically stable and accurate singular value decomposition. The algorithm is easily applied to slowly time-varying systems using windowing or exponential weighting.