An unified theory for collective behavior of cooperative system

This paper works on the collective behavior of affine nonlinear multi-agent dynamic systems under time-varying directed network. Based on the notion called time-invariant adjoint graph we further define intermittent connectivity, strongly intermittent connectivity, independent-strongly intermittent component, and so on. Every independent-strongly intermittent component corresponds to a minimal sub-system of multi-agent system or called independent basic subsystem of system. Under some minor conditions each independent basic subsystem will reach their own consensus state. All states of the system reach consensus if and only if there is only one independent basic subsystem of the system. These results generalize the previous works on affine multi-agent dynamic systems under time-invariant directed network.