# Modal Barriers to Controllability in Networks with Linearly-Coupled Homogeneous Subsystems

arXiv: https://arxiv.org/abs/1805.01995 · HTML: https://mlsanity.com/paper/1805.01995/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2018.

## Built on by (most cited first, 1 of 1)

- [Partial Excitation in Parameter Learning](https://mlsanity.com/paper/2503.02235/) (2025)

## Abstract (arXiv)

The controllability of networks comprising homogeneous multi-input multi-output linear subsystems with linear couplings among them is examined, from a modal perspective. The eigenvalues of the network model are classified into two groups: 1) network-invariant modes, which have very high multiplicity regardless of the network's topology; and 2) special-repeat modes, which are repeated for only particular network topologies and have bounded multiplicity. Characterizations of both types of modes are obtained, in part by drawing on decentralized-fixed-mode and generalized-eigenvalue concepts. We demonstrate that network-invariant modes necessarily prevent controllability unless a sufficient fraction of the subsystems are actuated, both in the network as a whole and in any weakly-connected partition. In contrast, the multiplicities of special-repeat modes have no influence on controllability. Our analysis highlights a distinction between built networks where subsystem interfaces may be unavoidable barriers to controllability, and multi-agent systems where protocols can be designed to ensure controllability.