Consensus of linear network systems diffusively coupled with exogenous disturbances: An ℋ∞ approach

This paper addresses the consensus control problem in multi‐agent systems under the influence of diffusively coupled disturbances. Two different types of systems are considered regarding the homogeneity of the disturbance coupling parameters. The main goal is to derive conditions that guarantee the prescribed performance of the designed control system on disturbance attenuation. To estimate the disturbance attenuation performance of the controller, the ℋ∞$$ {\mathscr{H}}_{\infty } $$ norm of the transfer function from the redefined disturbance vector to the disagreement vector is measured. Then the sufficient conditions for the system to achieve consensus within the desired performance are derived in terms of linear matrix inequalities (LMI). Numerical examples of both one‐ and multi‐dimensional consensus control systems are provided to check the validity of the derived LMI feasibility test along with the illustration of consensus behavior in time domain.