08/12/2020 – 14h00-15h00 – Online
The multiplicity-induced-dominancy property for scalar differential equations with time-delays
Abstract. Even in simple situations with time-delays such as that of linear equations with constant coefficients and constant delays, the spectral analysis of time-delay systems can be a challenging question. Indeed, contrarily to the delay-free situation in which Routh–Hurwitz criterion allows for handy characterizations of the location of spectral values in terms of the coefficients of the system, time-delay systems have infinitely many spectral values and there is no explicit link between these values and the coefficients of the system.
Some recent works have highlighted an interesting property of time-delay systems, called multiplicity-induced-dominancy (MID): for some families of time-delay systems, a spectral value of maximal multiplicity is necessarily the rightmost spectral value in the complex plane, and hence determines the asymptotic behavior of the system. Since then, an important research effort was made to identify families of time-delay systems satisfying the MID property.
After an introductory discussion on the spectral analysis of time-delay systems, this talk will present the MID property and some families of systems for which it is known to hold. We will also illustrate its application to the stabilization of control systems and present the main perspectives of this ongoing line of research. This talk is based on joint works with Amina Benarab, Catherine Bonnet, Islam Boussaada, Silviu-Iulian Niculescu, Karim Trabelsi, and Tomáš Vyhlídal.
Biography. After his Engineering degrees from the São Carlos School of Engineering, University of São Paulo, Brazil, and from École Polytechnique, France, Guilherme Mazanti obtained his Master’s degree on Applied Mathematics at École Polytechnique in 2013 and his Ph.D. on Applied Mathematics also at École Polytechnique, University Paris–Saclay, in 2016, after defending his thesis on the stability and control of linear switched systems in finite and infinite dimensions.
From September 2016 until August 2019, he was a postdoctoral fellow at the Laboratory of Mathematics of Orsay, University of Paris-Sud, working mostly on the analysis of minimal-time mean field games. From September 2019 until September, 2020, he was a postdoctoral researcher in a joint project of the Polytechnic Institute of Applied Sciences (IPSA), of Inria research center Saclay – Île-de-France, and of CentraleSupélec’s Laboratory of Signals and Systems (L2S), working on the stabilization of time-delay systems.
He is currently a researcher at Inria, at the Saclay – Île-de-France research center, and part of the team « Dynamical Interconnected Systems in Complex Environments » (DISCO). He is also a member of the Laboratory of Signals and Systems (L2S) at CentraleSupélec. His main research interest is on control theory, with several research topics lying between applied mathematics and engineering, such as stabilization and asymptotic behavior of time-delay systems, control and stabilization of hyperbolic PDEs, mean field games, and switched systems.
Practical details. The seminar will take place online, using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online Automatiques seminars), and if you do not already have access to the AutoSeminar group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » AutoSeminar channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.