H ∞ consensus for multi-agent systems with restricted frequency-domain specifications

This paper considers the H ∞ consensus problem with restricted frequency-domain specifications (RFDs) of multi-agent systems. Using a linear transformation, the consensus problem is first transformed into a partial stability problem of a reduced dimensional system. Then the sufficient and necessary conditions are given for H ∞ consensus with RFDs in directed networks, subject to parameter uncertainties and external disturbances. Moreover, the state feedback controller gain is achieved by a alternating iteration algorithm. A numerical example is presented to illustrate the effectiveness of the proposed approach.