A Geometrical Strategy for the Identification of State Space Models of Linear Multivariable Systems with Singular Value Decomposition

Abstract

In this paper, 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 to estimate the order of the observable part of the system and its state space model matrices. Moreover, conditions for persistance 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 to quantify these concepts. An example of an industrial plant identification is presented.