# Controllability of ensembles of linear dynamical systems

arXiv: https://arxiv.org/abs/1504.06167 · HTML: https://mlsanity.com/paper/1504.06167/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2015.

## Built on by (most cited first, 2 of 2)

- [Constructive Universal Approximation and Finite Sample Memorization by Narrow Deep ReLU Networks](https://mlsanity.com/paper/2409.06555/) (2024)
- [Ensemble Recognition in Reproducing Kernel Hilbert Spaces through Aggregated Measurements](https://mlsanity.com/paper/2112.14307/) (2021)

## Abstract (arXiv)

We investigate the task of controlling ensembles of initial and terminal state vectors of parameter-dependent linear systems by applying parameter-independent open loop controls. Necessary, as well as sufficient, conditions for ensemble controllability are established, using tools from complex approximation theory. For real analytic families of linear systems it is shown that ensemble controllability holds only for systems with at most two independent parameters. We apply the results to networks of linear systems and address the question of open-loop robust synchronization.