# System Norm Regularization Methods for Koopman Operator Approximation

@article{Dahdah2021SystemNR, title={System Norm Regularization Methods for Koopman Operator Approximation}, author={Steven Dahdah and James Richard Forbes}, journal={ArXiv}, year={2021}, volume={abs/2110.09658} }

Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this paper, Extended Dynamic Mode Decomposition (DMD) and DMD with control, two popular methods for approximating the Koopman operator, are reformulated as convex optimization problems with linear matrix inequality constraints. Hard asymptotic stability constraints and…

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