Identification of linear time-varying systems

This paper is concerned with the identification of linear time-varying systems. The discrete-time state space model of freely vibrating systems is used as an identification model. The focus is placed on identifying successive discrete transition matrices that have the same eigenvalues as the original transition matrices. First a typical subspace-based method is presented to illustrate the extraction of the observability range space using the singular value decomposition (SVD) of a general Hankel matrix. Then, the identification of varying transition matrices is approached by using an ensemble of response sequences. For arbitrarily varying systems, a series of the Hankel matrices are formed by an ensemble set of responses which are obtained through multiple experiments on the system with the same time-varying behavior. The varying transition matrix at each moment is estimated through the SVD of two successive Hankel matrices. The proposed algorithm is applied to two special cases that require only a single response series, i.e., periodically varying systems and slowly varying systems. The use of the eigenvalues of the transition matrices is discussed and the pseudomodal parameters are defined. Finally, a two-link manipulator subjected to a varying end force is used as an example to illustrate the tracking capability and performance of the proposed algorithm. (C) 1997 Academic Press Limited.