A numerically stable dynamic mode decomposition algorithm for nearly defective systems

M. Thitsa, M. Clouatre, E. Verriest, S. Coogan, C. Martin
IEEE Control Systems Letters, Jan. 2021


The potential for numerical instabilities of Dynamic Mode Decomposition (DMD), which assumes the completeness of the eigenspace is discussed for cases where the underlying system is defective or nearly defective. A numerically stable approach based on Schur decomposition is presented. The proposed method complements the DMD for cases where eigendecomposition is ill- conditioned. Both mathematical analysis and the results of numerical experiments are presented.