  In the context of event-triggered control, the timing of the triggering
events carries information about the state of the system that can be used for
stabilization. At each triggering event, not only can information be
transmitted by the message content (data payload) but also by its timing. We
demonstrate this in the context of stabilization of a laboratory-scale inverted
pendulum around its equilibrium point over a digital communication channel with
bounded unknown delay. Our event-triggering control strategy encodes timing
information by transmitting in a state-dependent fashion and can achieve
stabilization using a data payload transmission rate lower than what the
data-rate theorem prescribes for classical periodic control policies that do
not exploit timing information. Through experimental results, we show that as
the delay in the communication channel increases, a higher data payload
transmission rate is required to fulfill the proposed event-triggering policy
requirements. This confirms the theoretical intuition that a larger delay
brings a larger uncertainty about the value of the state at the controller, as
less timing information is carried in the communication. In addition, our
results also provide a novel encoding-decoding scheme to achieve input-to-state
practically stability (ISpS) for nonlinear continuous-time systems under
appropriate assumptions.
