Les séminaires de l’équipe MODESTY ont lieu en collaboration avec l’équipe DISCO et permettent à des doctorants, postdoctorants et membres permanents de l’équipe de présenter leurs travaux les plus récents
29/06/2026 : Global Asymptotic Stability Certificates for Discrete-Time Lur’e Systems under Incremental-like Restrictions
Orateur : G. Montana
Résumé : In this talk, we discuss the stability analysis of MIMO discrete-time Lur’e systems using passivity-based methods. We present global asymptotic stability conditions for systems with decentralized multivariable nonlinearities satisfying incremental-based constraints. We also present preliminary results allowing to treat coupled multivariable nonlinearities. The developed approach simplifies the Lyapunov function certificates and thanks to a modified Kalman-Yakubovic-Popov lemma, we perform the search of the Lyapunov function parameters by solving Semi-definite programs.
04/05/2026 : Stabilization of networks of general first-order hyperbolic partial differential equations
Orateur : A. Braun
Résumé : This presentation introduces a novel methodology for the stabilization of networks of general first-order hyperbolic partial differential equations (PDEs). By means of a backstepping transformation, the original stabilization problem for the PDE network is recast as the stabilization of an associated integral difference equation (IDE). The feedback controller is then designed at the level of the IDE and is expressed in terms of integral operators acting on the state and input histories over a finite time horizon. Closed-loop stability is established through the characterization of the controller kernels as solutions of a convolution equation arising from a Corona problem. The existence of these solutions is guaranteed under an appropriate spectral stabilizability condition. A least-squares numerical procedure is subsequently employed to compute the controller kernels. The proposed approach is illustrated through the stabilization of a chain of three hyperbolic PDEs with two control inputs applied at arbitrary nodes of the network. Furthermore, a counterexample is provided to illustrate a case in which the stabilizability condition is not satisfied.
30/03/2026 : Control-oriented MID: stabilization of conservative mechanical systems via delayed state feedback
Orateur : T. Balogh
Résumé : Stabilization of linear time-invariant dynamical systems via delayed state feedback might be possible by assigning a multiple real root of the corresponding closed-loop characteristic quasi-polynomial. In this talk, we address sufficient conditions for the multiplicity-induced dominance (MID) of a real characteristic root if the parameters of the plant are fixed. These conditions can be investigated by exploiting the structure of the open-loop characteristic polynomial. The results will be demonstrated through specific examples of controlled mechanical systems.
23/02/2026 : Stability conditions for integral delay equations, a Lyapunov-Krasovskii approach
Orateur : R. Ortiz
Résumé : Contrary to differential delay equations, non-differential equations as difference equations in continuous time and integral delay equations are significantly less employed than their differential counterparts.The stability of integral delay equations (IDEs) is a central concern because they arise in the analysis and control of systems with delays: as the difference operator of neutral type delay systems or part of their interconnection formulation, as additional dynamics that result from using transformations to achieve sufficient delay-dependent stability conditions or as constrains on the controller gain, when approximating the integral of the finite spectrum assignment control law for input-delay systems. Integral delay equations also appear in modeling systems with propagation phenomena, for example, population and epidemic models described by the renewal equation and after performing certain transformations in systems described by hyperbolic partial differential equations In population models, IDEs make it possible to track the effective reproductive number, which is a parameter that helps to predict the behavior and deduce the stability of population dynamics. In fact, they have shown to have advantages over differential models in the identification of parameters from clinical data. The stability analysis of linear IDEs has been addressed from the perspective of the approach of Lyapunov-Krasovskii functionals. This approach extends the Lyapunov analysis for delay-free systems leading to the proposals of different functionals resulting in sufficient stability conditions in the form of Linear Matrix Inequalities (LMIs). However, the classical Lyapunov stability criterion for linear delay-free systems has been extended to linear time-delay systems producing a family of relatively simple necessary and sufficient stability conditions in terms of the delay Lyapunov matrix. IDEs are included in this family of stability conditions that involve testing the positivity of a symmetric block matrix with a specific structure.
