  We provide a Lyapunov-function-based method for establishing different types
of uniform input-to-state stability (ISS) for time-varying impulsive systems.
The method generalizes to impulsive systems with inputs the well-established
philosophy of assessing the stability of a system by reducing the problem to
that of the stability of a scalar system given by the evolution of the Lyapunov
function on the system trajectories. This reduction is performed in such a way
so that the resulting scalar system has no inputs. Novel sufficient conditions
for ISS are provided, which generalize existing results for time-invariant and
time-varying, switched and nonswitched, impulsive and nonimpulsive systems in
several directions.
