Extension of modal analysis to linear time-varying systems

Linear time-varying (LTV) systems have been often dealt with on a case-by-c ase basis. Many well-developed concepts and analytic methods of linear time -invariant (LTI) systems cannot be applied to LTV systems. For example, the conventional definition of modal parameters is invalid for LTV systems. Th e first part of this paper explores the possibility of extending the modal concept of LTV systems. The discrete-time state-space model is used to repr esent LTV systems. By analogy to LTI systems, the pseudo-modal parameters a re defined using the eigenvalues of the discrete-time state transition matr ix. The paper shows that the pseudo-modal parameters preserve certain prope rties of the conventional modal parameters defined for LTI systems. The sec ond part of the paper extends a previously developed algorithm to identify the pseudo-modal parameters using forced responses and forcing inputs. For a general LTV system, the input and output Hankel matrices formed by an ens emble of data satisfy a matrix facotrization relation. The key step of the method is to modify the output matrix in such a way that the range space of the observability matrix can be extracted. A robotic manipulator with vary ing inertia links is used as an example. The first part of the numerical si mulation illustrates the applications of the pseudo-modal parameters. The s econd part of the simulation tests the identification algorithm under diffe rent conditions. Several practical issues are addressed. (C) 1999 Academic Press.