Embedded Files
Hyperbolic PDEs: Controller and observer synthesis
Hyperbolic PDEs: Controller and observer synthesis
Hyperbolic partial differential equations model a wide range of complex dynamical systems, particularly in transport and wave propagation phenomena. In this context, the synthesis of closed-loop control laws and observers, notably via the complex triplet approach, aims to ensure that these systems meet prescribed performance and stability specifications.
Feedback linearization for the Clarifier
Feedback linearization for the Clarifier
Work in progress
PID Control for the Gantry Crane with saturation
PID Control for the Gantry Crane with saturation
L. Ma, N. Vanspranghe, D. Astolfi, V. Andrieu, M. Bajodek, X. Lou, Nested Saturation Proportional Derivative Control for Conservative PDE-ODE Interconnections: the Gantry Crane Example. In: Automatica. Volume 185, Issue 112834, 2026. <10.1016/j.automatica.2026.112834>
L. Ma, V. Andrieu, D. Astolfi, M. Bajodek, C.Z. Xu, X. Lou, « Integral action feedback design for conservative abstract systems in the presence of input nonlinearities ». In: IEEE Transactions on Automatic and Control, vol. 70, no. 11, pp. 7580-7587, 2025. <10.1109/TAC.2025.3574637>
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>
ODE-PDE interconnections
ODE-PDE interconnections
The interconnection of ordinary differential equations (ODEs) with partial differential equations (PDEs), especially through heterogeneous boundary conditions governed by ODE dynamics, leads to particularly challenging systems. Even in the linear case, their spectral properties and analytical solutions are generally unknown, which makes their study difficult. This motivates the development of new analytical and synthesis tools to better understand and control such coupled systems.
Control design for ODE-PDE interconnections
Control design for ODE-PDE interconnections
M. Bajodek, H. Lhachemi, and G. Valmorbida, « Design of low-dimensional controllers for high-dimensional systems ». In: Systems and Control Letters 198, 106049, 2025. <hal-04248781> <10.1016/j.sysconle.2025.106049>
Stability analysis for ODE-weak-hyperbolic-PDE
Stability analysis for ODE-weak-hyperbolic-PDE
M.O. Amirat, M. Bajodek, J. Auriol, V. Andrieu, C. Valentin, Insights into the stability analysis of 2-by-2 linear weakly hyperbolic systems. Submitted to Automatica.
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>
M. Bajodek, H. Lhachemi, and G. Valmorbida, « Necessary Stability Conditions for reaction-Diffusion-ODE Systems ». IEEE Transactions on Automatic and Control. <hal-04008999> <10.1109/TAC.2024.3407818>
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.
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>
A. Castaño, M. Bajodek, S. Mondié, « Legendre approximation-based stability test for distributed delay systems ». In: SIAM SINUM, Vol. 63, Issue 2, 2025. <hal-04923013> <10.1137/23M1610859>
G. Portilla, M. Bajodek, S. Mondié, « Necessary and sufficient condition for neutral-type delay systems: Polynomial approximations ». In: MCSS, 2025. <10.1007/s00498-025-00426-8>.
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>
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>
Page updated
Google Sites
Report abuse