  In this paper, a set-membership filtering-based leader-follower
synchronization protocol for discrete-time linear multi-agent systems is
proposed wherein the aim is to make the agents synchronize with a leader. The
agents, governed by identical high-order discrete-time linear dynamics, are
subject to unknown-but-bounded input disturbances. In terms of its own state
information, each agent only has access to measured outputs that are corrupted
with unknown-but-bounded output disturbances. Also, the initial states of the
agents are unknown. To deal with all these unknowns (or uncertainties), a
set-membership filter (or state estimator), having the `correction-prediction'
form of a standard Kalman filter, is formulated. We consider each agent to be
equipped with this filter that estimates the state of the agent and consider
the agents to be able to share the state estimate information with the
neighbors locally. The corrected state estimates of the agents are utilized in
the local control law design for synchronization. Under appropriate conditions,
the global disagreement error between the agents and the leader is shown to be
bounded. An upper bound on the norm of the global disagreement error is
calculated and shown to be monotonically decreasing. Finally, two simulation
examples are included to illustrate the effectiveness of the proposed
set-membership filter and the proposed leader-follower synchronization
protocol.
