# Strong Structural Controllability of Signed Networks

## TL;DR

This paper introduces a combinatorial approach to analyze and ensure the strong structural controllability of signed networks, focusing on eigenvalue multiplicities and zero forcing sets.

## Contribution

It proposes a new combinatorial condition for strong structural controllability of signed networks and bounds eigenvalue multiplicities.

## Key findings

- Introduces positive and negative signed zero forcing sets.
- Provides a sufficient condition for strong structural controllability.
- Establishes an upper bound on eigenvalue multiplicities.

## Abstract

In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a signed graph. In this direction, we introduce the notion of positive and negative signed zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a signed graph is provided.