Controllability of directed and matrix‐valued weighted networks

Abstract This paper studies the controllability of multi‐agent systems with directed and matrix‐valued weighted networks. Almost equitable partition theory is increasingly being chosen by researchers as a framework for controllability of multi‐agent systems from graph‐theoretic perspective. Based on the matrix‐valued almost equitable partition, we propose a graph‐theoretic characterization of the upper bounds of dimension of controllable subspace. Then, we provide graph‐theoretic necessary conditions for controllability and methods of constructing uncontrollable topologies. Several examples are given to illustrate these results.