Ph. D. Project
Methodological tools for the modeling and the analysis of interconnected hybrid systems
2019/10/01 - 2022/09/30
Other supervisor(s):
Hybrid systems are dynamical systems that exhibit both continuous-time and discrete-time evolutions. Examples
are broad and include sampled-data systems, mechanical systems with impacts, energy grids involving power
converters, biological systems etc. While powerful tools are nowadays available for the modeling and the stability
analysis of stand-alone hybrid systems, significant challenges arise when interconnecting several hybrid systems
together. This problem is of major importance as interconnected hybrid systems emerge in a variety of application
domains such as networks of cyber-physical systems, energy grids, and opinion dynamics to give only a few
examples, and we currently lack adapted tools to analyze their stability properties. The goal of this PhD will
therefore be to develop modeling and analysis tools, which are tailored for interconnected hybrid systems. The
idea is to derive global stability properties directly based on the local properties of each subsystem, and the
nature of the interconnections pattern, thereby drastically facilitating the analysis. Case studies from opinion
dynamics and cyber-physical systems will be investigated to validate the proposed theory.
Hybrid systems, interconnected systems, stability, Lyapunov methods, networked systems
Duration: 3 years
Location: CRAN, Vandoeuvre-lès-Nancy (France) during 2 years, and LAAS-CNRS, Toulouse (France) during 1 year.
This is flexible according to the PhD student's requirements.
Salary: around 1600¬/month (net)

We are looking for a strongly motivated candidate having a M.Sc. degree or equivalent degree in control
engineering, or applied mathematics with a pronounced taste for methodological research. The candidate has to
be familiar with Matlab (or an equivalent software), and to be fluent in English.
Control Identification Diagnosis