Contributed by: Wim Michiels,Wim.Michiels@cs.kuleuven.be
PhD position on ”Control oriented analysis of linear periodic delay-differential algebraic systems”
Delay-differential algebraic equations (DDAEs) naturally appear in mathematical models for dynamical systems. A systematic description of the components of the system and their interconnections leads to a combination of differential equations and algebraic constraints, while the delays model the inherent timelags in the interconnections. The analysis of systems described by DDAEs is challenging due to the interplay between the implicit system description and the infinite-dimensional dynamics. At the same time, the literature is very limited and scattered over different domains.
The project aims at the construction of an overarching mathematical framework for the analysis of linear time-invariant and time-periodic DDAEs. First, the basic theory will be addressed, contributing to stability and Floquet theory, and to perturbation theory. Second, analysis methods and computational tools will be constructed to assess and optimize the robustness of the stationary solution.
Distinct features in the methodology are the role of duality, in a system theoretic sense, and connections with nonlinear eigenvalue problems. In order to reach the objectives, the theories of differential equations, matrix distance problems, algebraic decision problems, and robust control approaches will be integrated.
The ideal candidate has a Master degree in mathematics (pure, applied, computational), mathematical engineering, or control engineering (with a strong interest in systems and control theory). Applicants whose mother tongue is not English, must present an official language test report.
We offer fully funded PhD position in an international context for four years at the Numerical Analysis and Applied Mathematics (NUMA) section of KU Leuven, a top European university and hub for interdisciplinary research in the fields of Applied Mathematics and Systems & Control.
More information, and application instructions can be found at https://www.kuleuven.be/personeel/jobsite/jobs/56124430
