27 citations · 60 across the 21 of their papers we have counts for
22 papers
Factor-parity Hall sets and controllability
Karine Beauchard, Frédéric Marbach
We introduce a class of Hall sets, which we call factor-parity Hall sets, whose elements split into good and bad brackets. We prove that the good brackets can be steered simultaneo…
Some quartic control results for scalar-input systems
Karine Beauchard, Frédéric Marbach
We investigate the role of quartic terms in the small-time local controllability of scalar-input systems. First, we prove a new sufficient condition for controllability, which expl…
Convergent realizations of Lie subalgebras
Karine Beauchard, Jérémy Le Borgne, Frédéric Marbach
It has been known since the seminal work of Guillemin and Sternberg that Lie subalgebras of finite codimension of an arbitrary real or complex Lie algebra can be realized as subalg…
Local convergence of Sussmann's infinite product for analytic vector fields
Jérémy Le Borgne, Frédéric Marbach
In 1986, Sussmann proposed an expansion of the Chen series as an infinite product of exponentials of Hall basis elements multiplied by coefficients defined through a simple inducti…
Time-iteration methods for controllability
Frédéric Marbach
These notes are based on a short course delivered at the Summer School EUR MINT 2025 "Control, Inverse Problems and Spectral Theory", held in June 2025 in Toulouse, France. The cou…
Nonlinear Forward-Backward Problems
Anne-Laure Dalibard, Frédéric Marbach, Jean Rax
We prove the existence and uniqueness of strong solutions to the equation in the vicinity of the linear shear flow, subject to perturbations of the source term…