Analyse et commande des modèles linéaires implicites 2D

Yeganefar; France; Sur place; EUR 40 000 - 60 000; Plein temps

Résumé du poste

A research organization in France is seeking a Mathematics Researcher to explore multidimensional systems and their stability analysis. Ideal candidates will hold a Master's in automation or applied mathematics, possess strong analytical skills, and be proficient in Matlab. This position offers an opportunity to contribute to advancing theoretical understanding and practical applications in mathematics. The role involves independent research and collaboration within a dedicated team.

Qualifications

• Master's degree in automation or applied mathematics, engineer in automatic control.
• Strong mathematical background in algebra and analysis.
• Strong desire to dig into somewhat mathematical problems.
• Proficiency in programming, particularly in Matlab.
• Good communication skills in English.
• Ability to conduct research independently.

Responsabilités

• Review the existing literature and state of the art.
• Possibly revisit the defined notions and associated formalism.
• Extend the class of models under study.
• Propose relevant and numerically applicable stability analysis tools.
• Propose synthesis methods for reasonably complex control laws.
• Optionally, propose concrete applications for the proposed tools.

Connaissances

Strong mathematical background in algebra and analysis

Proficiency in programming, particularly in Matlab

Good communication skills in English

Ability to conduct research independently

Formation

Master's degree in automation or applied mathematics

Description du poste

Organisation/Company Yeganefar Research Field Engineering Mathematics Researcher Profile Recognised Researcher (R2) Leading Researcher (R4) First Stage Researcher (R1) Established Researcher (R3) Country France Application Deadline 9 Apr 2026 - 22:00 (UTC) Type of Contract Temporary Job Status Full-time Offer Starting Date 1 Oct 2026 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Is the Job related to staff position within a Research Infrastructure? No

Offer Description

Multidimensional systems (or nD systems) are models where information propagates not only along one dimension, traditionally time, but across several dimensions, which can be represented by a combination of spatial or temporal variables. In this respect, they belong to the class of infinite-dimensional systems and present new theoretical challenges. To understand these new difficulties, the case of 2D systems (with two dimensions) alone is a reservoir of theoretical problems.

The two most studied linear 2D models in the literature are the Roesser model and the Fornasini-Marchesini model, for which the team has, in recent years, analyzed three notions of stability in the case where both dimensions are discrete: asymptotic stability, exponential stability, and structural stability, as well as the existing relationships between these three notions. Ongoing work is currently being done to establish a continuous counterpart to the results obtained in the discrete case.

However, "more concrete" cases, such as those inspired from simple partial differential equations, highlight the need to introduce generalised models, particularly an implicit version of the Roesser model. This model leads, among other things, to intermediate definitions of stability, which do not exactly correspond to the notions defined in the classical (explicit) case. Indeed, if one dimension is spatial and the other temporal, stability can be understood as convergence along the temporal dimension only, even though the model remains intrinsically 2D. Thus, the notion of structural stability becomes too strong because it treats both dimensions equally, and it should be relaxed to give meaning to the study. Furthermore, the concept of causality in space does not exist, which clearly shows that the two dimensions should not always be approached in the same way. A special case of interest would be the case where the “temporal” dimension is continuous while the “space” dimension is discrete.

Work has already been carried out on this subject, but the A&S team of LIAS would like to continue in this direction by further exploring the implicit model and deepening the various definitions of stability.

The doctoral work will consist of:

• Reviewing the existing literature and state of the art;
• Possibly revisiting the defined notions and the associated formalism to bring more coherence to the study;
• Extending the class of models under study;
• Proposing relevant and numerically applicable stability analysis tools;
• Proposing synthesis methods for reasonably complex control laws;
• Optionally, proposing concrete applications for the proposed tools.

Desired profile:

• Master's degree in automation or applied mathematics, engineer in automatic control
• Strong mathematical background in algebra and analysis
• Strong desire to "dig into" somewhat mathematical problems
• Proficiency in programming, particularly in Matlab
• Good communication skills in English
• Ability to conduct research independently