Diagonalization algorithms for linear time-varying dynamic systems

On the basis of a mode-vector representation, we show that its time-varying amplitudes and frequencies can be obtained by diagonalizing the system mat rix. Next, we reformulate an explicit diagonalizing algorithm that was earl ier proposed by Wu. Then, the missing convergence proof is given. Moreover, we present a new and implicit iteration scheme that is closely related to that given by Wu. In both algorithms, the time-varying system matrix is gra dually diagonalized by successive algebraic similarity transformations. It is proved that the convergence conditions are essentially the same. Althoug h the class of systems for which the algorithms are applicable is still not fully known, the results of this paper may be of theoretical and practical interest.