# Zero controllability in discrete-time structured systems

## TL;DR

This paper explores how to select minimal driver nodes in discrete-time complex networks to ensure controllability near a linearization point, using graph-based conditions and algorithms.

## Contribution

It introduces graph-based conditions and an algorithm for selecting minimal driver nodes to achieve controllability in nonlinear discrete-time networks.

## Key findings

- Conditions for controllability via driver nodes are derived.
- An algorithm for minimal driver node selection is proposed.
- The approach ensures the network can be steered close to linearization.

## Abstract

In this paper we consider complex dynamical networks modeled by means of state space systems running in discrete time. We assume that the dependency structure of the variables within the (nonlinear) network equations is known and use directed graphs to represent this structure. The dependency structure also appears in the equations of a linearization of the network. In order for such a linearization to be a good approximation of the original network, its state should stay as close as possible to the point of linearization. In this paper, we investigate how the latter can be achieved by an appropriate selection of states as driver nodes, so that through these driver nodes the whole state of the network can be steered to the point of linearization. We present conditions in graph terms for this to be possible and derive an algorithm for the associated driver node selection, possibly of smallest size.