Subspace-based identification for linear and nonlinear systems

This paper deals with the basic subspace algorithm for time-invariant systems. A simplified proof of the fact that the state sequence and/or the observability matrix of the dynamical system can be determined directly from input-output data is provided. Some existing identification algorithms for linear time-varying systems are presented. The paper also covers the bulk of the existing subspace-based nonlinear identification algorithms including Hammerstein and nonlinear feedback identification, Hammerstein-Wiener identification for Wiener systems, linear parameter-varying system identification, and bilinear system identification.