# Linear programming-based stabilization and synchronization of positive complex networks with dynamic link subsystems

## TL;DR

This paper presents a new method using linear programming to stabilize and synchronize complex networks with dynamic links.

## Contribution

A novel coupling term and stabilization framework for positive complex networks using linear programming.

## Key findings

- A new coupling term ensures stability and synchronization of positive complex networks.
- A simulation example confirms the effectiveness of the proposed approaches.
- Linear programming and copositive Lyapunov functions enable tractable design and analysis.

## Abstract

This paper investigates the stabilization and synchronization of positive complex networks with dynamic links. A class of positive complex networks is constructed by introducing dynamic link between nodes. A controller and the corresponding coupling term with respect to links are designed to achieve the positivity and stability of complex networks and link systems, respectively. Then, a synchronization controller and the corresponding coupling term with respect to links and node states are proposed, respectively. The main contributions are as follows: (i) A novel coupling term is constructed to achieve stability and synchronization of positive complex networks, (ii) A stabilization and synchronization framework is constructed by designing two classes of controllers and coupling terms, and (iii) A tractable design, analysis, and computation method is introduced by virtue of linear programming and copositive Lyapunov function. Finally, a simulation example is provided to verify the effectiveness and feasibility of the proposed approaches.