  In analysis and control of large-scale nonlinear dynamical systems, a
distributed approach is often an attractive option due to its computational
tractability and usually low communication requirements. Success of the
distributed control design relies on the separability of the network into
weakly interacting subsystems such that minimal information exchange between
subsystems is sufficient to achieve satisfactory control performance. While
distributed analysis and control design for dynamical network have been well
studied, decomposition of nonlinear networks into weakly interacting subsystems
has not received as much attention. In this article we propose a vector
Lyapunov functions based approach to quantify the energy-flow in a dynamical
network via a model of a comparison system. Introducing a notion of power and
energy flow in a dynamical network, we use sum-of-squares programming tools to
partition polynomial networks into weakly interacting subsystems. Examples are
provided to illustrate the proposed method of decomposition.
