  This paper develops a robust dynamic mode decomposition (RDMD) method endowed
with statistical and numerical robustness. Statistical robustness ensures
estimation efficiency at the Gaussian and non-Gaussian probability
distributions, including heavy-tailed distributions. The proposed RDMD is
statistically robust because the outliers in the data set are flagged via
projection statistics and suppressed using a Schweppe-type Huber generalized
maximum-likelihood estimator that minimizes a convex Huber cost function. The
latter is solved using the iteratively reweighted least-squares algorithm that
is known to exhibit a better convergence property and numerical stability than
the Newton algorithms. Several numerical simulations using canonical models of
dynamical systems demonstrate the excellent performance of the proposed RDMD
method. The results reveal that it outperforms several other methods proposed
in the literature.
