Strong Sign Controllability of Diffusively-Coupled Networks

TL;DR

This paper establishes conditions for strong sign controllability in diffusively-coupled undirected networks, providing methods to analyze basic components, extend to larger graphs, and optimize input node placement.

Contribution

It introduces necessary and sufficient conditions for strong sign controllability of basic network components and develops an efficient algorithm for minimal input node selection.

Findings

Conditions for strong sign controllability of paths, cycles, and trees.

A merging process to extend controllability to larger networks.

An algorithm with polynomial complexity for minimal input node determination.

Abstract

This paper presents several conditions to determine strong sign controllability for diffusively-coupled undirected networks. The strong sign controllability is determined by the sign patterns (positive, negative, zero) of the edges. We first provide the necessary and sufficient conditions for strong sign controllability of basic components, such as path, cycle, and tree. Next, we propose a merging process to extend the basic componenets to a larger graph based on the conditions of the strong sign controllability. Furthermore, we develop an algorithm of polynomial complexity to find the minimum number of external input nodes while maintaining the strong sign controllability of a network.