Oberseminar "Dynamische Systeme und Kontrolltheorie" - Irina Alexandrova

Delay Lyapunov matrix is an analogue of solution V to the classical Lyapunov matrix equation A^T V +
V A = −W for linear time-invariant time delay systems. Recently, a number of necessary and sufficient
stability tests, which depend exclusively on the Lyapunov matrix and may be verified by a finite
number of operations, appeared in the literature. In those tests, stability analysis of a time delay
system is reduced to verification of positive definiteness of a certain block matrix which is based on
the Lyapunov matrix values at some discretization points. In this talk, we give an overview of existing
tests and discuss the directions of future research in the field.