Distributed $H_{\infty}$ control of interconnected systems subject to networked gossip protocol and packet dropout

This paper studies the distributed
$H_{\infty}$
control problems for interconnected systems subject to networked gossip protocol and packet dropout. In interconnected systems, the communication among different sub-controllers are subject to gossip protocol, which means that each sub-controller communicates with only one randomly chosen neighbor instead of communicating with all neighbors at each instant. Furthermore, this paper also considers the packet dropout phenomenon in the communication network. According to Lyapunov method, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to ensure the exponentially mean-square stability with
$H_{\infty}$
performance of the closed-loop system. Distributed controllers can be designed by solving the obtained LMIs. Finally, the effectiveness and superiority of the proposed method are proved by two numerical examples.