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This paper considers the distributed robust suboptimal consensus controlproblem of linear multi-agent systems, with both H2 and H_infty performancerequirements. A novel two-step complementary design approach is proposed. Inthe first step, a distributed control law is designed for the nominalmulti-agent system to achieve consensus with a prescribed H2 performance. Inthe second step, an extra control input, depending on some carefully chosenresidual signals indicating the modeling mismatch, is designed to complementthe H2 performance by providing robustness guarantee in terms of H_inftyrequirement with respect to disturbances or uncertainties. The proposedcomplementary design approach provides an additional degree of freedom fordesign, having two separate controls to deal with the H2 performance and therobustness of consensus, respectively. Thereby, it does not need to make muchtrade-off, and can be expected to be much less conservative than the trade-offdesign such as the mixed H2/H_infty control method. Besides, this complementaryapproach will recover the achievable H2 performance when external disturbancesor uncertainties do not exist. The effectiveness of the theoretical results andthe advantages of the complementary approach are validated via numericalsimulations.

Distributed Optimal Control with Recovered Robustness for Uncertain Network Systems: A Complementary Design Approach