# Sampled-Data Exponential Synchronization of Complex Dynamical Networks with Saturating Actuators

## TL;DR

This paper presents a new method for synchronizing complex networks with delays and input saturation using a sampled-data controller.

## Contribution

A novel memory sampled-data controller and modified two-sided looped functional are introduced for exponential synchronization.

## Key findings

- A memory sampled-data controller is designed to handle transmission delay effects.
- A modified two-sided looped functional improves synchronization criteria.
- An optimization algorithm is proposed to enlarge the region of attraction.

## Abstract

This paper investigates the problem of exponential synchronization control for complex dynamical systems (CDNs) with input saturation. Considering the effects of transmission delay, a memory sampled-data controller is designed. A modified two-sided looped functional is constructed that takes into account the entire sampling period, which includes both current state information and delayed state information. This functional only needs to be positive definite at the sampling instants. Sufficient criteria and the controller design method are provided to ensure the exponential synchronization of CDNs with input saturation under the influence of transmission delay, as well as the estimation of the basin of attraction. Additionally, an optimization algorithm for enlarging the region of attraction is proposed. Finally, a numerical example is presented to verify the effectiveness of the conclusion.