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

Robust Consensus Analysis and Design under Relative State Constraints or Uncertainties