  In this paper, we first establish an exponential stability result for a class
of linear switched systems and then apply this result to show the existence of
the distributed observer for a discrete-time leader system over jointly
connected switching networks. A special case of this result leads to the
solution of a leader-following consensus problem of multiple discrete-time
double-integrator systems over jointly connected switching networks. Then, we
further develop the adaptive distributed observer for the discrete-time leader
system over jointly connected switching networks, which has the advantage over
the distributed observer in that it does not require that every follower know
the system matrix of the leader system. As an application of the discrete-time
distributed observer, we will solve the cooperative output regulation problem
of a discrete-time linear multi-agent system over jointly connected switching
networks. A leader-following formation problem of mobile robots will be used to
illustrate our design. This problem cannot be handled by any existing approach.
