  This paper considers the synchronization problem for networks of coupled
nonlinear dynamical systems under switching communication topologies. Two types
of nonlinear agent dynamics are considered. The first one is non-expansive
dynamics (stable dynamics with a convex Lyapunov function $\varphi(\cdot)$) and
the second one is dynamics that satisfies a global Lipschitz condition. For the
non-expansive case, we show that various forms of joint connectivity for
communication graphs are sufficient for networks to achieve global asymptotic
$\varphi$-synchronization. We also show that $\varphi$-synchronization leads to
state synchronization provided that certain additional conditions are
satisfied. For the globally Lipschitz case, unlike the non-expansive case,
joint connectivity alone is not sufficient for achieving synchronization. A
sufficient condition for reaching global exponential synchronization is
established in terms of the relationship between the global Lipschitz constant
and the network parameters. We also extend the results to leader-follower
networks.
