Numerical Algorithms for Subspace State Space Systemidentification ( N 4 Sid )

We present the basic notions on subspace identiication algorithms for linear systems. These methods estimate state sequences or extended observability matrices directly from the given data, through an orthogonal or oblique projection of the row spaces of certain block Hankel matrices into the row spaces of others. The extraction of the state space model is then achieved through the solution of a least squares problem. These algorithms can be elegantly implemented using well-known numerical linear algebra algorithms such as the LQ-and singular value decomposition. The paper aims at giving an overview of the methodologies used in time domain subspace identiication. A short overview of frequency domain subspace identiication results is also presented.