In Chap. 4, we have studied state synchronization for networked nonlinear dynamical systems under switching communication topologies. Sufficient conditions are established in terms of connectivity, nonlinear self-dynamics, and the network parameters. On the other hand, a stronger condition can be obtained for the case where the nonlinear agent dynamics are non-expansive dynamics, i.e., stable dynamics with a convex Lyapunov function φ(⋅). In particular, we show that several forms of joint connectivity for communication graphs are sufficient for networks to achieve global asymptotic φ-synchronization in this chapter.