# Controllability of Directed Heterogeneous Networked MIMO Systems

## TL;DR

This paper establishes new controllability criteria for directed heterogeneous networked MIMO systems, revealing that heterogeneity in node dynamics can enable controllability even when homogeneous networks are uncontrollable.

## Contribution

It provides the first necessary and sufficient controllability condition for heterogeneous networked MIMO LTI systems, expanding understanding beyond homogeneous network criteria.

## Key findings

- Heterogeneous networks can be controllable even if homogeneous counterparts are not.
- A necessary and sufficient condition for controllability is derived.
- Controllability depends on network topology, node dynamics, and inner interactions.

## Abstract

This paper studies the controllability of networked multi-input-multi-output (MIMO) systems, in which the network topology is weighted and directed, and the nodes are heterogeneous higher-dimensional linear time-invariant (LTI) dynamical systems. The primary objective is to search for controllability criteria beyond those already known for homogeneous networks. The focus is on the effects of the network topology, node dynamics, external control inputs, as well as the inner interactions on the network controllability. It is found that a network of heterogeneous systems can be controllable even if the corresponding homogeneous network topology is uncontrollable. The finding thus unravels another fundamental property that affects the network controllability---the heterogeneity of the node dynamics. A necessary and sufficient condition is derived for the controllability of heterogeneous networked MIMO LTI systems. For some typical cases, necessary and/or sufficient controllability conditions are specified and presented on the node dynamics, inner interactions, as well as the network topology.