M. Bajodek, A. Seuret, and F. Gouaisbaut, “Stability analysis of an ordinary differential equation interconnected with the reaction-diffusion equation”. In: Automatica 145, p. 110515, 2022. <doi: 10.1016/j.automatica.2022.110515> <hal-03150194>
C. Kitsos, M. Bajodek, and L. Baudouin, « Joint coefficient and solution estimation for the 1D wave equation: An observer-based solution to inverse problems ». In: IEEE Transactions on Automatic Control 68(8), p. 4827-4840, 2022. <doi: 10.1109/TAC.2022.3213625> <hal-03447113>
The stability results are based on frequency analysis or Lyapunov analysis. By extension of the finite-dimensional state with Legendre polynomials coefficients, we present sufficient conditions of stability. Thanks to Fourier-Legendre remainder convergence, we proved some conditions become necessary and sufficient for sufficiently large orders.
M. Bajodek, F. Gouaisbaut, and A. Seuret, « On the necessity of sufficient LMIs conditions for time-delay systems arising from Legendre approximation ». In: Automatica (159), 111322, 2024. <hal-04008999> <doi:10.1016/j.automatica.2023.111322>
M. Bajodek, F. Gouaisbaut, and A. Seuret, « Necessary and sufficient stability condition for time-delay systems arising from Legendre approximation ». In: IEEE Transactions on Automatic Control 68 (10), p. 6262-6269, 2022. <hal-03435028> <doi:10.1109/TAC.2022.3232052>
M. Bajodek, F. Gouaisbaut, A. Seuret, « Frequency delay-dependent stability criterion for time-delay systems thanks to Fourier-Legendre remainders ». In: International Journal of Robust and Nonlinear Control 31(12), p. 5813-5831, 2021. <doi:10.1002/rnc.5575> <hal-03218016>
The main idea was to determine porosity profiles from reflected signals. A fast time domain relfectometry inversion was developed using:
– A conjugate gradient method to invert the finite-difference time-domain model of the telegrapher’s equations,
– a geometrical model for a coaxial line,
– a mixing rule to give a link between permittivity and porosity.
Once calibrated and validated, the algorithm was used to observe porosity changes.
V.S.R. Annapareddy, A. Sufian, T. Bore, M. Bajodek, and A. Scheuermann, « Computation of local permeability in gap-graded granular soils ». In: Géotechnique Letters 12(1), p. 68-73, 2022. <doi:10.1680/jgele.21.00131>
A. Sufian, T. Bittner, T. Bore, M. Bajodek, and A. Sheuermann, « Physical observations of the transient evolution of the porosity distribution during internal erosion using spatial TDR ». In: Canadian Geotechnical Journal 59(8), 2022. <doi:10.1139/cgj-2021-0570>
T. Bittner, M. Bajodek, T. Bore, E. Vourc’h, and A. Sheuermann, « Determination of the porosity distribution during an erosion test using a coaxial line cell ». In: Sensors 19(3), 611, 2019. <doi:10.3390/s19030611>
L. Yermán, T. Bore, M.L. Serna, S. Zárate, T. Bittner, M. Bajodek, and A. Scheuermann, « Integration of Time Domain Reflectometry in a smouldering reactor ». In: Chemical Engineering Research and Design 138, p. 34-38, 2018. <doi : 10.1016/j.cherd.2018.09.018>