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ODE-PDE interconnections
ODE-PDE interconnections
Stability analysis for ODE-reaction-diffusion
Stability analysis for ODE-reaction-diffusion
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>
Observer synthesis for the wave equation
Observer synthesis for the wave equation
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>
Time-delay systems: Stability conditions
Time-delay systems: Stability conditions
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.
LMI condition
LMI condition
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>
Positivity condition
Positivity condition
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>
Frequency condition
Frequency condition
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>
Time domain reflectometry inversion
Time domain reflectometry inversion
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.
Porosity profile
Porosity profile
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>
Water profile in a smouldering reactor
Water profile in a smouldering reactor
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>
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