  By designing the decentralized time-regularized (Zeno-free) event-triggered
strategies for the state-feedback control law, this paper considers the
stochastic stabilization of a class of networked control systems, where two
sources of randomness exist in multiple decentralized networks that operate
asynchronously and independently: the communication channels are constrained by
the stochastic network delays and also by Poisson pulsing denial-of-service
(Pp-DoS) attacks. The time delay in the network denotes the length from a
transmission instant to the corresponding update instant, and is supposed to be
a continuous random variable subject to certain continuous probability
distribution; while the attacks' cardinal number is a discrete random variable
supposed to be subject to Poisson distribution, so the inter-attack time, i.e.,
the time between two consecutive attack instants, is subject to exponential
distribution. The considered system is modeled as a stochastic hybrid
formalism, where the randomness enters through the jump map into the reset
value (the inter-attack time directly related) of each triggered strategy. By
only sampling/transmitting state measurements when needed and simultaneously by
taking the specific medium access protocols into account, the designed
event-triggered strategies are synthesized in a state-based and decentralized
form, which are robust (tolerable well) to stochastic network delays, under
different tradeoff-conditions between the minimum inter-event times, maximum
allowable delays (i.e., potentially tolerable delays) and the frequencies of
attacks. Using stochastic hybrid tools to combine attack-active parts with
attack-over parts, the designed triggered strategies, if designed well
according to the actual system needs, can tolerate (be resilient to) the Pp-DoS
attacks and stochastic network delays without jeopardizing the stability and
Zeno-freeness.
