  This study focuses on event-triggered control of nonlinear discrete-time
systems with time delays. Based on a Lyapunov-Krasovskii type input-to-state
stability result, we propose a novel event-triggered control algorithm that
works as follows. The control inputs are updated only when a certain
measurement error surpasses a dynamical threshold depending on both the system
states and the evolution time. Sufficient conditions are established to ensure
that the closed-loop system maintains its asymptotic stability. It is shown
that the time-dependent portion in the dynamical threshold is essential to
derive the lower bound of the times between two consecutive control updates. As
a special case of our results, we demonstrate the performance of the designed
event-triggering algorithm for a class of linear control systems with time
delays. Numerical simulations are provided to demonstrate the effectiveness of
our algorithm and theoretical results.
