Consensus algorithms for multi-agent systems: A matrix inequality based approach

In this paper, we study a consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. Existing approaches in the literature are mostly based on graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods can not deal with complicated control specification. For this purpose, we propose to reduce the consensus problem on hand to solving a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and then propose two algorithms for solving the matrix inequality. It turns out that our approach includes the existing Laplacian based approach as a special case, and can deal with various additional control requirements such as convergence rate specification and actuator limitations.