  We provide a distributed coordinated approach to the stability analysis and
control design of large-scale nonlinear dynamical systems by using a vector
Lyapunov functions approach. In this formulation the large-scale system is
decomposed into a network of interacting subsystems and the stability of the
system is analyzed through a comparison system. However finding such comparison
system is not trivial. In this work, we propose a sum-of-squares based
completely decentralized approach for computing the comparison systems for
networks of nonlinear systems. Moreover, based on the comparison systems, we
introduce a distributed optimal control strategy in which the individual
subsystems (agents) coordinate with their immediate neighbors to design local
control policies that can exponentially stabilize the full system under initial
disturbances.We illustrate the control algorithm on a network of interacting
Van der Pol systems.
