The goal of this paper is to investigate stability of consensus control of linear multi-agent systems with periodically switched communication topologies. To this end, our contribution is to exploit Floquet theory as a main tool to investigate the stability of consensus problem for a switched system that consists of a set of linear time invariant subsystems and a periodic switching rule. The Lyapunov stability analysis for discrete-time systems is also discussed to confirm the results of utilizing Floquet theory. The simulation results are illustrated for the cases with single-integrator dynamics, double-integrator dynamics and leader-follower consensus problem.