This article investigates the synthesis of distributed economic control algorithms under which dynamically coupled physical systems are regulated to a variational equilibrium of a constrained convex game. We study two complementary cases: 1) each subsystem is linear and controllable and 2) each subsystem is nonlinear and in the strict-feedback form. The convergence of the proposed algorithms is guaranteed using the Lyapunov analysis. Their performance is verified by two case studies on a multizone building temperature regulation problem and an optimal power flow problem, respectively.