  This paper proposes a new approach to analyze and design distributed robust
consensus control protocols for general linear leaderless multi-agent systems
(MASs) in presence of relative-state constraints or uncertainties. First, we
show that the MAS robust consensus under relative-state constraints or
uncertainties is equivalent to the robust stability under state constraints or
uncertainties of a transformed MAS. Next, the transformed MAS under state
constraints or uncertainties is reformulated as a network of Lur'e systems. By
employing S-procedure, Lyapunov theory, and Lasalle's invariance principle, a
sufficient condition for robust consensus and the design of robust consensus
controller gain are derived from solutions of a distributed LMI convex problem.
Finally, numerical examples are introduced to illustrate the effectiveness of
the proposed theoretical approach.
