Research project granted by The Swedish Research Council
The Swedish Research Council has published this year's approved applications for research projects in natural and engineering science. Professor Bo Kågström at The Department of Computing Science was granted 3 400 000 SEK in funds for the research project “Stratification of matrix pencils with structure”. The research is conducted in collaboration with PhD Stefan Johansson and PhLicentiate Andrii Dmytryshyn.
All together 15 projects at Umeå University were granted.
The Swedish Research Council is a government agency that provides funding for basic research of the highest scientific quality in all disciplinary domains.
Abstract in English
We address challenging problems of how canonical forms of structured matrix pencils change under structure-preserving perturbations. Our goal is to provide a flexible framework for analyzing matrix pencils with structured matrices, which includes stratifications (construction of closure hierarchies) of matrix pencils with different types of symmetries and block structures.
Structured matrix pencils appear in the design and analysis of dynamical systems and can be found in a wide range of applications. The discretized models often have structured matrices with a physical meaning, which are important to preserve in the simulations as well during the analyses. Examples are system pencils in control, symmetric/skew-symmetric matrix pencils, and polynomial matrix linearizations associated with higher order systems.
The broad range of new structure-preserving methods demands new theory and methods for analyzing structured perturbations, which is a strong motivation for our research. We build novel stratification theory which provides the complete picture of nearby canonical structures and how structure transitions take place under structure-preserving perturbations. The outcome is novel theories, algorithms, and software tools, which are applicable to the analyses of dynamical systems and supply information for a deeper understanding of how the system characteristics can change under perturbations.
