We present topological obstructions to the existence of C¹ stabilizing feedback laws for control systems of the form ẋ = f(x, u), subject to the constraint that the system function f and the feedback law u are assumed to depend only on selected subsets of the state variables. Such constraints arise naturally in the context of distributed control systems, and the topological obstructions are expressed in terms of the generators of certain homology groups associated with the control problem.