Research
My research interests include nonlinear systems in general, and in particular: dynamical systems, control theory, stochastic processes, and robotics.
Specific topics related to my work: feedback stabilization, Koopman operator theory, datadriven algorithms, closed oneforms in dynamics, Morse/Conley theory, stochastic processes and topology, invariant manifolds, bifurcations, differential flatness, geometric mechanics, and hybrid systems.
Published or accepted journal papers:

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. 19691974. (article, 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 generalization of the Hopf degree theorem.
Matthew D. Kvalheim.
Proceedings of the American Mathematical Society, 151.1 (2023), pp. 453–454. (article, arXiv) 
Planning of obstacleaided navigation for multilegged robots using a samplingbased method over directed graphs.
Kaustav Chakraborty, Haodi Hu, Matthew D. Kvalheim, and Feifei Qian.
IEEE Robotics and Automation Letters, 7.4 (2022), pp. 88618868. (article) 
Necessary conditions for feedback stabilization and safety.
Matthew D. Kvalheim and Daniel E. Koditschek.
Journal of Geometric Mechanics, 14.4 (2022), pp. 659693. (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) 
Families of periodic orbits: closed 1forms and global continuability.
Matthew D. Kvalheim and Anthony M. Bloch.
Journal of Differential Equations, 285 (2021), pp. 211257. (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. 784825. (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. 22492270. (article, arXiv) 
Global linearization and fiber bundle structure of invariant manifolds.
Jaap Eldering, Matthew D. Kvalheim, and Shai Revzen.
Nonlinearity, 31.9 (2018), pp. 42024245. (article, arXiv)
Published or accepted peerreviewed conference papers:

The role of symmetry in constructing geometric flat outputs for freeflying robotic systems.
Jake Welde, Matthew D. Kvalheim, and Vijay Kumar.
IEEE International Conference on Robotics and Automation, Accepted (2023). (arXiv) 
Generic properties of Koopman eigenfunctions for stable fixed points and periodic orbits.
Matthew D. Kvalheim, David Hong, and Shai Revzen.
IFACPapersOnline, 54.9 (2021), pp. 267272. (article, arXiv)

Datadriven 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, ButterworthHeinemann, Elsevier, Oxford (2017). (link) 
Locomotion as an oscillator.
Shai Revzen and Matthew D. Kvalheim.
Bioinspired legged locomotion, Ch. 3.5, ButterworthHeinemann, Elsevier, Oxford (2017). (link)
Papers under review and selected other preprints:

Why do autoencoders work?.
Matthew D. Kvalheim and Eduardo D. Sontag.
(2023). (arXiv) 
Koopman embedding and superlinearization counterexamples with isolated equilibria.
Philip Arathoon and Matthew D. Kvalheim.
(2023). (arXiv) 
Linearizability of flows by embeddings.
Matthew D. Kvalheim and Philip Arathoon.
(2023). (arXiv) 
Estimating phase from observed trajectories using the temporal 1form.
Simon Wilshin, Matthew D. Kvalheim, Clayton Scott, and Shai Revzen.
(2022). (arXiv) 
Phase response curves and the role of coordinates.
Simon Wilshin, Matthew D. Kvalheim, and Shai Revzen.
(2021). (arXiv) 
A pasting lemma for Lipschitz functions.
Matthew D. Kvalheim, Paul Gustafson, and Samuel A. Burden.
(2021). (arXiv) 
PoincaréHopf theorem for hybrid systems.
Matthew D. Kvalheim.
(2021). (arXiv)
PhD thesis:
Aspects of invariant manifold theory and applications, 207 pages, December 2018. (link)
Selected talks:
 M. Kvalheim. “Discovering engineering (im)possibilities with geometry and topology.” Invited talk, University of Pennsylvania GRASP SFI Seminar (2023). Philadelphia, PA, USA. (video, slides)
 M. Kvalheim. “Asymptotic stabilizability.” Invited talk, BIRS workshop Geometry, Topology and Control System Design (2023). Banff, AB, Canada. (slides)
 M. Kvalheim. “Existence and uniqueness of Koopman eigenfunctions near stable equilibria and limit cycles.” Invited talk, International Symposium on Nonlinear Theory and Its Applications (NOLTA 2022). Online. (slides)
 M. Kvalheim. “Large deviations, persistent homology, and Brownian conductors with negative resistance.” Invited talk, Cornell University Probability Seminar (2022). Online.
 M. Kvalheim. “When can hybrid systems operate safely?” Invited talk, University of Michigan Control Seminar (2022). Online.
 M. Kvalheim. “Flux in small noise dynamics: persistence and negative resistance.” Invited talk, Brown University, Division of Applied Mathematics (2022). Online.
 S. Burden and M. Kvalheim. “When and how are hybrid dynamical systems conjugate to their classical quotients?” Invited talk, SIAM Conference on Control and its Applications (2021). Online.
 M. Kvalheim. “Towards a Conley theory for hybrid dynamical systems.” Invited talk, Rutgers TRIPODS/DATAINSPIRE Workshop on Dynamics, Topology, and Robotic Control (2021). Online. (video)
 M. Kvalheim. “Hierarchical Composition via Collapse of Dimension in Dynamical Systems.” Invited talk, ETH Zürich Autonomy Talks (2021). Online.
 A. M. Bloch and M. Kvalheim. “Geometry and dynamics of circulant systems.” Invited talk, AMS sectional meeting, special session on Geometric Dynamics (2020). Online.
 M. Kvalheim, P. Gustafson, D. Koditschek. “Toward a task planning theory for robot hybrid dynamics.” Invited talk, BIRSCMO workshop on Topological Complexity and Motion Planning (2020). Online.
 M. Kvalheim, S. Wilshin, C. Scott, and S. Revzen. “Isochrons from short, noisy data. Invited talk, Dynamics Days Europe (2020). Online.
 M. Kvalheim and S. Revzen. “Reducedorder models for locomotion in the perturbed Stokes regime.” Invited talk, SIAM Conference on Applications of Dynamical Systems (2019). Snowbird, UT.