Synchronization of multi-agent systems via static output feedback control

In this paper, we propose a distributed static output feedback to investigate the synchronization problem of multi-agent systems subject to exogenous disturbance. By introducing the augmented representation of the closed-loop system, we can decouple the controller matrix from the system matrices and the Lyapunov matrix. Necessary and sufficient conditions are established to ensure that the multi-agent systems achieve synchronization and has a prescribed H∞ attenuation level. Slack matrices are adopted to induce more flexibility for the obtained conditions. Furthermore, an iteration algorithm is proposed to solve the obtained conditions. Finally, we present a numerical example to demonstrate the effectiveness and merits of the proposed techniques.