The MODESTY team’s seminars are held in collaboration with the DISCO team and allow doctoral students, postdoctoral researchers, and permanent team members to present their most recent work.
23/02/2026 : Stability conditions for integral delay equations, a Lyapunov-Krasovskii approach
Speaker: R. Ortiz
Abstract: 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.
