  We study the dynamics of systems on networks from a linear algebraic
perspective. The control theoretic concept of controllability describes the set
of states that can be reached for these systems. Under appropriate conditions,
there is a connection between the quantum (Lie theoretic) property of
controllability and the linear systems (Kalman) controllability condition. We
investigate how the graph theoretic concept of a zero forcing set impacts the
controllability property. In particular, we prove that if a set of vertices is
a zero forcing set, the associated dynamical system is controllable. The
results open up the possibility of further exploiting the analogy between
networks, linear control systems theory, and quantum systems Lie algebraic
theory. This study is motivated by several quantum systems currently under
study, including continuous quantum walks modeling transport phenomena.
Additionally, it proposes zero forcing as a new notion in the analysis of
complex networks.
