The existing results on the leaderless and leader-following consensus problems for discrete-time linear multi-agent systems subject to jointly connected switching networks are limited to undirected networks. This note will first study the stability property for a class of discrete-time linear switched systems. This stability result will then be applied to the two consensus problems for discrete-time linear multi-agent systems subject to directed jointly connected switching networks. It is shown that, in some interesting cases, the two problems are solvable by the distributed state feedback control law even if the switching networks are directed and every time disconnected.