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