Oberseminar "Dynamische Systeme und Kontrolltheorie" - Ivan Atamas

This article proposes an approach to construction of the Lyapunov function for a linear coupled impulsive
system consisting of two time-invariant subsystems. In this case, in contrast to various variants of small-gain
stability conditions for coupled systems, the presence of the asymptotic stability property of independent
subsystems is not assumed. To analyze the asymptotic stability of a coupled system, the direct Lyapunov
method is used in combination with the discretization method. The periodic case and the case when the
Floquet theory is not applicable at all are considered separately. The main results are illustrated with
examples.