  This paper studies input-to-state stability (ISS) of general nonlinear
time-delay systems subject to delay-dependent impulse effects. Sufficient
conditions for ISS are constructed by using the method of Lyapunov functionals.
It is shown that, when the continuous dynamics are ISS but the discrete
dynamics governing the delay-dependent impulses are not, the impulsive system
as a whole is ISS provided the destabilizing impulses do not occur too
frequently. On the contrary, when the discrete dynamics are ISS but the
continuous dynamics are not, the delayed impulses must occur frequently enough
to overcome the destabilizing effects of the continuous dynamics so that the
ISS can be achieved for the impulsive system. Particularly, when the discrete
dynamics are ISS and the continuous dynamics are also ISS or just stable for
the zero input, the impulsive system is ISS for arbitrary impulse time
sequences. Compared with the existing results on impulsive time-delay systems,
the obtained ISS criteria are more general in the sense that these results are
applicable to systems with delay dependent impulses while the existing ones are
not. Moreover, when consider time-delay systems with delay-free impulses, our
result for systems with unstable continuous dynamics and stabilizing impulses
is less conservative than the existing ones, as a weaker condition on the upper
bound of impulsive intervals is obtained. To demonstrate the theoretical
results, we provide two examples with numerical simulations, in which
distributed delays and discrete delays in the impulses are considered,
respectively.
