Subspace Techniques in System Identification

Abstract

An overview is given of the class of subspace techniques (STs) for identifying linear, time-invariant state-space models from input-output data. STs do not require a parametrization of the system matrices and as a consequence do not suffer from problems related to local minima that often hamper successful application of parametric optimization-based identification methods. The overview follows the historic line of development. It starts from Kronecker's result on the representation of an infinite power series by a rational function and then addresses, respectively, the deterministic realization problem, its stochastic variant, and finally the identification of a state-space model given in innovation form. The overview summarizes the fundamental principles of the algorithms to solve the problems and summarizes the results about the statistical properties of the estimates as well as the practical issues like choice of weighting matrices and the selection of dimension parameters in using these STs in practice. The overview concludes with probing some future challenges and makes suggestions for further reading.