On subspace identification of the extended observability matrix

A lower left Q-orthogonal (LQ) decomposition is often used in order to compute certain projections of the known data matrices and to estimate the extended observability matrix from the column space (range) of a projected matrix. An alternative method based on the partial least squares (PLS) method is presented in this paper. A Monte Carlo simulation experiment of a MIMO system is presented in order to compare the method with two other subspace methods presented in the literature. In addition some new results in subspace identification are proved. Consistency of the estimate of the extended observability matrix is also addressed