  Input-to-state stability (ISS) allows estimating the impact of inputs and
initial conditions on both the intermediate values and the asymptotic bound on
the solutions. ISS has unified the input-output and Lyapunov stability theories
and is a crucial property in the stability theory of control systems as well as
for many applications whose dynamics depend on parameters, unknown
perturbations, or other inputs. In this habilitation thesis, we provide a broad
picture of infinite-dimensional input-to-state stability theory.
