Research

Interests: dynamical systems, control theory, differential topology, and applications.

Selected preprints:

• Differential topology of the spaces of asymptotically stable vector fields and Lyapunov functions.
  Matthew D. Kvalheim.
  (2025). (arXiv)

• Autoencoding dynamics: topological limitations and capabilities.
  Matthew D. Kvalheim and Eduardo D. Sontag.
  (2025). (arXiv)

• Koopman embedding and super-linearization counterexamples with isolated equilibria.
  Philip Arathoon and Matthew D. Kvalheim.
  (2023). (arXiv)

Published or accepted journal papers:

• Linearizability of flows by embeddings.
  Matthew D. Kvalheim and Philip Arathoon.
  Selecta Mathematica, Accepted (2025). (arXiv)

• Estimating phase from observed trajectories using the temporal 1-form.
  Simon Wilshin, Matthew D. Kvalheim, Clayton Scott, and Shai Revzen.
  Cover article, Neural Computation, 37.12 (2025), pp. 2158–2204. (article, outdated arXiv)

• Global linearization of asymptotically stable systems without hyperbolicity.
  Matthew D. Kvalheim and Eduardo D. Sontag.
  Systems and Control Letters, 203 (2025), pp. 106163. (article, arXiv)

• Why should autoencoders work?.
  Matthew D. Kvalheim and Eduardo D. Sontag.
  Transactions on Machine Learning Research (2024), pp. 1–24. (article, arXiv)

• Phase response curves and the role of coordinates.
  Simon Wilshin, Matthew D. Kvalheim, and Shai Revzen.
  Biological Cybernetics, 118 (2024), pp. 311–330. (article, outdated arXiv)

• Flux in tilted potential systems: negative resistance and persistence.
  Yuliy Baryshnikov and Matthew D. Kvalheim.
  Communications in Mathematical Physics, 400.2 (2023), pp. 853–930. (article, arXiv)

• Obstructions to asymptotic stabilization.
  Matthew D. Kvalheim.
  SIAM Journal on Control and Optimization, 61.2 (2023), pp. 536–542. (article, arXiv)

• A compositional approach to certifying the almost global asymptotic stability of cascade systems.
  Jake Welde, Matthew D. Kvalheim, and Vijay Kumar.
  IEEE Control Systems Letters, 7 (2023), pp. 1969–1974. (article, arXiv)

• A generalization of the Hopf degree theorem.
  Matthew D. Kvalheim.
  Proceedings of the American Mathematical Society, 151.1 (2023), pp. 453–454. (article, arXiv)

• Necessary conditions for feedback stabilization and safety.
  Matthew D. Kvalheim and Daniel E. Koditschek.
  Journal of Geometric Mechanics, 14.4 (2022), pp. 659–693. (article, arXiv)
  Invited contribution to special volume honoring Anthony Bloch on his 65th birthday.

• Planning of obstacle-aided navigation for multi-legged robots using a sampling-based method over directed graphs.
  Kaustav Chakraborty, Haodi Hu, Matthew D. Kvalheim, and Feifei Qian.
  IEEE Robotics and Automation Letters, 7.4 (2022), pp. 8861–8868. (article)

• Families of periodic orbits: closed 1-forms and global continuability.
  Matthew D. Kvalheim and Anthony M. Bloch.
  Journal of Differential Equations, 285 (2021), pp. 211–257. (article, arXiv)

• Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits.
  Matthew D. Kvalheim and Shai Revzen.
  Physica D, 425 (2021), pp. 132959. (article, arXiv)

• Conley’s fundamental theorem for a class of hybrid systems.
  Matthew D. Kvalheim, Paul Gustafson, and Daniel E. Koditschek.
  SIAM Journal on Applied Dynamical systems, 20.2 (2021), pp. 784–825. (article, arXiv)

• Gait modeling and optimization for the perturbed Stokes regime.
  Matthew D. Kvalheim, Brian Bittner, and Shai Revzen.
  Nonlinear Dynamics, 97.4 (2019), pp. 2249–2270. (article, arXiv)

• Global linearization and fiber bundle structure of invariant manifolds.
  Jaap Eldering, Matthew D. Kvalheim, and Shai Revzen.
  Nonlinearity, 31.9 (2018), pp. 4202–4245. (article, arXiv)

Published or accepted peer-reviewed conference papers:

• Relationships between necessary conditions for feedback stabilizability.
  Matthew D. Kvalheim.
  Geometry, Topology, and Control System Design: Proceedings of a Banff International Research Station Workshop (2025), pp. 167–179. (book, arXiv)

• The role of symmetry in constructing geometric flat outputs for free-flying robotic systems.
  Jake Welde, Matthew D. Kvalheim, and Vijay Kumar.
  IEEE International Conference on Robotics and Automation (2023), pp. 12247–12253. (article, arXiv)

• Generic properties of Koopman eigenfunctions for stable fixed points and periodic orbits.
  Matthew D. Kvalheim, David Hong, and Shai Revzen.
  IFAC-PapersOnline, 54.9 (2021), pp. 267–272. (article, arXiv)

• Data-driven models of legged locomotion.
  Shai Revzen and Matthew D. Kvalheim.
  SPIE Defense + Security, International Society for Optics and Photonics (2015). (article)

Book chapters:

• Templates and anchors.
  Matthew D. Kvalheim and Shai Revzen.
  Bioinspired legged locomotion, Ch. 3.2, Butterworth-Heinemann, Elsevier, Oxford (2017). (link)

• Locomotion as an oscillator.
  Shai Revzen and Matthew D. Kvalheim.
  Bioinspired legged locomotion, Ch. 3.5, Butterworth-Heinemann, Elsevier, Oxford (2017). (link)

PhD thesis:

Aspects of invariant manifold theory and applications, 207 pages, December 2018. (link)