**Sergey Dashkovskiy (Universität Bremen)**

### Title: Stability of interconnected nonlinear large scale systems with inputs

We consider nonlinear systems with inputs. Each system is
assumed to be stable in a certain sense, that will be explained. Our main
question is whether an interconnection of these systems remains stable. We
will start with introduction of input-to-state stability (ISS) notion and
known facts about ISS systems and illustrate them with simple examples. A
sufficient condition for the stability of an interconnection of systems
will be given and discussed. A constructive method of finding a Lyapunov
function will be shown. We will see how the derivation of our main results
is related to monotone operators and some purely topological problems. In
the end we will provide several application examples of the main results
coming from different engineering problems

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