Project
Control oriented analysis of linear periodic delay-differential algebraic equations
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 time-lags in the interconnections. The analysis of systems described by DDAEs is challenging due to the interplay between the implicit system description and the infinitedimensional 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 project exploits the unique position of the applicant’s group at the intersection of systems theory and computational mathematics.