This article addresses the distributed consensus problem of linear multi-agent systems with discontinuous observations over a time-invariant undirected communication topology. Under the assumption that each agent can only intermittently share its outputs with the neighbours, a class of distributed observer-type of protocols are designed and utilised to achieve consensus. By using appropriate matrix decomposition, it is shown that consensus in the closed-loop multi-agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent. From a multiple Lyapunov functions approach, it is proved that there exists a protocol to guarantee consensus if the communication time rate is larger than a threshold value. Furthermore, a distributed pinning control method is employed to solve the consensus problem on an arbitrary given topology which needs not be connected. Particularly, the questions of what kind of agents and at least how many agents should be pinned are addressed. The effectiveness of the analytical results is finally verified by numerical simulations.