  Input-to-state stability (ISS) unifies global asymptotic stability with
respect to variations of initial conditions with robustness with respect to
external disturbances. First, we present Lyapunov characterizations for
input-to-state stability as well as ISS superpositions theorems showing
relations of ISS to other robust stability properties. Next, we present one of
the characteristic applications of the ISS framework - the design of
event-based control schemes for the stabilization of nonlinear systems. In the
second half of the paper, we focus on small-gain theorems for stability
analysis of finite and infinite networks with input-to-state stable components.
First, we present a classical small-gain theorem in terms of trajectories for
the feedback interconnection of 2 nonlinear systems. Finally, a recent
Lyapunov-based small-gain result for a network with infinitely many ISS
components is shown.
