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Researcher profile

Antoine Chaillet

Antoine Chaillet contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.OCeess.SYmath.DSSystems and ControlNeurons and Cognition

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Published work

5 published item(s)

preprint2026arXiv

A Mathematical Characterization of Neural Activation Induced by Temporal Interference Stimulation

Temporal Interference Stimulation (TIS) is a non-invasive neuromodulation technique in which two high-frequency sinusoidal currents with slightly different frequencies generate a low-frequency envelope that can activate deep neural structures. This study investigates the conditions under which TIS elicits action potentials in a single neuron modeled by the FitzHugh-Nagumo system. This research integrates phase-plane analysis and geometric singular perturbation to develop a mathematical framework for analyzing TIS. By combining a mathematical analysis of differential equations with computer simulations, the study elucidates how the amplitudes and beat frequency jointly determine whether the neuron remains quiescent, exhibits only transient responses, or undergoes persistent (tonic) firing.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Existence of an equilibrium for delayed neural fields under output proportional feedback

Recently, [2] proved that the closed-loop system resulting from the output proportional feedback stabilization of a class of delayed neural fields is input-to-state stable (ISS) for sufficiently high gain, subject to the existence of an equilibrium point for the closed-loop system. In the present paper, we show that a sufficient condition for such an equilibrium to exist is that the activation functions are bounded.

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preprint2022arXiv

Growth conditions for global exponential stability and exp-ISS of time-delay systems under point-wise dissipation

For time-delay systems, it is known that global asymptotic stability is guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates in a point-wise manner along solutions, namely whose dissipation rate involves only the current value of the solution's norm. So far, the extension of this result to global exponential stability (GES) holds only for systems ruled by a globally Lipschitz vector field and remains largely open for the input-to-state stability (ISS) property. In this paper, we rely on the notion of exponential ISS to extend the class of systems for which GES or ISS can be concluded from a point-wise dissipation. Our results in turn show that these properties still hold in the presence of a sufficiently small additional term involving the whole state history norm. We provide explicit estimates of the tolerable magnitude of this extra term and show through an example how it can be used to assess robustness with respect to modeling uncertainties.

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preprint2022arXiv

Is Global Asymptotic Stability Necessarily Uniform for Time-Delay Systems?

For time-invariant finite-dimensional systems, it is known that global asymptotic stability (GAS) is equivalent to uniform global asymptotic stability (UGAS), in which the decay rate and transient overshoot of solutions are requested to be uniform on bounded sets of initial states. This paper investigates this relationship for time-invariant delay systems. We show that UGAS and GAS are equivalent for this class of systems under the assumption of robust forward completeness, i.e. under the assumption that the reachable set from any bounded set of initial states on any finite time horizon is bounded. We also show that, if the state space is a space in a particular family of Sobolev or Holder spaces, then GAS is equivalent to UGAS and that robust forward completeness holds. Based on these equivalences, we provide a novel Lyapunov characterization of GAS (and UGAS) in the aforementioned spaces.

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preprint2015arXiv

Global stabilization of multiple integrators by a bounded feedback with constraints on its successive derivatives

In this paper, we address the global stabilization of chains of integrators by means of a bounded static feedback law whose p first time derivatives are bounded. Our construction is based on the technique of nested saturations introduced by Teel. We show that the control amplitude and the maximum value of its p first derivatives can be imposed below any prescribed values. Our results are illustrated by the stabilization of the third order integrator on the feedback and its first two derivatives.

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