  In this work, we consider the problem of event-triggered implementation of
control laws designed for the local stabilization of nonlinear systems with
center manifolds. We propose event-triggering conditions which are derived from
a local input-to-state stability characterization of such systems. The
triggering conditions ensure local ultimate boundedness of the trajectories and
the existence of a uniform positive lower bound for the inter-event times. The
ultimate bound can be made arbitrarily small, but by allowing for smaller
inter-event times. Under certain assumptions on the controller structure, local
asymptotic stability of the origin is also guaranteed. Two sets of triggering
conditions are proposed, that cater to the cases where the exact center
manifold and only an approximation of the center manifold is computable. The
closed-loop system exhibits some desirable properties when the exact knowledge
of the center manifold is employed in checking the triggering conditions. Three
illustrative examples that explore different scenarios are presented and the
applicability of the proposed methods is demonstrated. The third example
concerns the event-triggered implementation of a position stabilizing
controller for the open-loop unstable Mobile Inverted Pendulum (MIP) robot.
