Research stay at UC3M: DEPARTMENT OF MATHEMATICS
Project: Theoretical and Numerical Methods for Matrix Problems arising in Control, Dynamical Systems, and Complex Networks.
This research project presents several open problems that will allow me to collaborate with several investigators of the research groups “Numerical Linear Algebra and Matrix Theory” and "Mathematics Applied to Control, Systems, and Signals" of the Universidad Carlos III.
The study of dynamical systems and networks heavily relies on the analysis of polynomial system models, and more specifically on standard and/or generalized state space models. Even though the theory behind these polynomial models is quite well understood, there are still important numerical issues that need to be addressed: algorithms used to compute the various structural elements of these models are still quite sensitive to perturbations and have a computational cost that is often too high. In this project we focus on several such problems and propose new algorithms with improved robustness and complexity properties. These problems include the development of a new canonical form for polynomial matrices, the study of robustness issues of dynamical systems in state space form, and the solution of special matrix equations for complex networks with special structure.
Fecha de estancia: DEC 2013 - JUL 2014