Periodic Event-Triggered Synchronization for Discrete-Time Complex Dynamical Networks

In this article, we investigate the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs). First, a discrete-time version of periodic event-triggered mechanism (ETM) is proposed, under which the sensors sample the signals in a periodic manner. But whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM. Compared with the common ETMs in the field of discrete-time systems, the proposed method avoids monitoring the measurements point-to-point and enlarges the lower bound of the inter-event intervals. As a result, it is beneficial to save both the energy and communication resources. Second, the ``discontinuous'' Lyapunov functionals are constructed to deal with the sawtooth constraint of sampling signals. The functionals can be viewed as the discrete-time extension for those discontinuous ones in continuous-time fields. Third, sufficient conditions for the ultimately bounded synchronization are derived for the discrete-time CDNs with or without considering communication delays, respectively. A calculation method for simultaneously designing the triggering parameter and control gains is developed such that the estimation of error level is accurate as much as possible. Finally, the simulation examples are presented to show the effectiveness and improvements of the proposed method.

Automated summary

This article investigates the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs), proposing a method that avoids point-to-point monitoring of measurements and enlarges the lower bound of inter-event intervals. "Discontinuous" Lyapunov functionals are constructed to handle the sawtooth constraint of sampling signals, and sufficient conditions for ultimately bounded synchronization are derived for the networks with or without considering communication delays. The method is shown effective and improvements are demonstrated through simulation examples.