TABLE OF CONTENTS The problem of identifying an LTI state-space model from input and output measurements of a dynamic system, which we analyzed in the previous two chapters, is re-addressed in this chapter via a completely different approach. The approach we take is indicated in the literature (Verhaegen, 1994; Viberg, 1995; Van Overschee and De Moor, 1996b; Katayama, 2005) as the class of subspace identification methods. These methods are based on the fact that, by storing the input and output data in structured block Hankel matrices, it is possible to retrieve certain subspaces that are related to the system matrices of the signal-generating state-space model. Examples of such subspaces are the column space of the observability matrix, Equation (3.25) on page 67, and the row space of the state sequence of a Kalman filter. In this chapter we explain how subspace methods can be used to determine the system matrices of a linear time-invariant system up to a similarity transformation. Subspace methods have also been developed for the identification of linear parameter-varying systems (Verdult and Verhaegen, 2002) and certain classes of nonlinear systems. The interested reader should consult Verdult (2002) for an overview.
Unlike with the identification algorithms presented in Chapters 7 and 8, in subspace identification there is no need to parameterize the model. Furthermore, the system model is obtained in a noniterative way via the solution of a number of simple linear-algebra problems. The key linear-algebra steps are an RQ factorization, an SVD, and the solution of...
