Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems areinherentlyrelated to the representation theory of algebras over fields. We will show thatanycontrol scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.