Quantum mechanics

Detector

Control (management)

Statistics

Event (particle physics)

Constraint (computer-aided design)

Telecommunications

Computer science

Bounded function

Computer network

Physics

Mathematics

Synchronization networks

Sampling (signal processing)

Discrete time and continuous time

Synchronization (alternating current)

Mathematical analysis

Artificial intelligence

Geometry

Sawtooth wave

Dynamical systems theory

Channel (broadcasting)

Control theory (sociology)

Computer vision

IEEE Transactions on Neural Networks and Learning Systems

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.

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