On the Surprising Effectiveness of Spectrum Clipping in Learning Stable Linear Dynamics

When learning stable linear dynamical systems from data, three important properties are desirable: i) predictive accuracy, ii) provable stability, and iii) computational efficiency. Unconstrained minimization of reconstruction errors leads to high accuracy and efficiency but cannot guarantee stability. Existing methods to enforce stability often preserve accuracy, but do so only at the cost of increased computation. In this work, we investigate if a straightforward approach can simultaneously offer all three desiderata of learning stable linear systems. Specifically, we consider a post-hoc approach that manipulates the spectrum of the learned system matrix that was computed using unconstrained least squares. We call this approach spectrum clipping (SC) as it involves eigen decomposition and subsequent reconstruction of the system matrix after clipping any eigenvalues that are larger than one to one (without altering the eigenvectors). Through comprehensive experiments involving two different applications and publicly available benchmark datasets, we show that this simple technique can efficiently learn highly-accurate linear systems that are provably-stable. Notably, we find that SC can match or outperform strong baselines while being orders-of-magnitude faster. We also show that SC can be readily combined with Koopman operators to learn stable nonlinear dynamics, such as those underlying complex dexterous manipulation skills involving multi-fingered robotic hands. Finally, we find that SC can learn stable robot policies even when the training data includes unsuccessful or truncated demonstrations. Our codes and dataset can be found atthis https URL.

@article{guo2025_2412.01168,
  title={ On the Surprising Effectiveness of Spectrum Clipping in Learning Stable Linear Dynamics },
  author={ Hanyao Guo and Yunhai Han and Harish Ravichandar },
  journal={arXiv preprint arXiv:2412.01168},
  year={ 2025 }
}