  This work studies analysis and synthesis problems for diffusively coupled
multi-agent systems. We focus on networks comprised of multi-input multi-output
nonlinear systems that posses a property we term maximal
equilibrium-independent cyclically monotonone passivity (MEICMP), which is an
extension of recent passivity results. We demonstrate that networks comprised
of MEICMP systems are related to a pair of dual network optimization problems.
In particular, we show that the steady-state behavior of the multi-agent system
correspond to the minimizers of appropriately defined network optimization
problems. Exploiting this connection between the dynamic networked system and
static optimization problems, we propose a synthesis procedure for designing
the coupling controllers in the network to achieve a desired output state for
the network. We provide detailed examples of dynamical networked systems
satisfying these properties and demonstrate the results for a network of damped
planar oscillators.
