A geometrical approach for the identification of state space models with singular value decomposition

Some geometrically inspired concepts are studied for the identification of models for multivariable linear time-invariant systems from noisy input-output observations. Starting from a fundamental highly structured input-output matrix equation, it is shown how the singular value decomposition allows the order of the observable part of the system and its state-space model matrices to be estimated. Moreover, conditions for persistency of excitation of the inputs and the behavior of the algorithm when the data are perturbed by noise can easily be studied from a geometrical point of view. The singular values allow these concepts to be quantified. An example with an industrial plant identification is presented