This paper considers the output synchronization of a class of networked agents. Each agent is a passive system. Local information, used by each agent to adjust its movement, forms a network with switching adjacent topology. First, we consider the asymptotic stability of nonlinear time-varying switched systems by using multiple Lyapunov function. An extended Lyapunov-like Lemma for switched systems is obtained. Then the result is applied to the output synchronization of a class of networked passive systems with switching topology. A pretty fair sufficient condition is presented.