Output regulation problem of multi-agents in networked systems

In this study, the output regulation problem of multi-agent systems in fixed topologies is analysed. The agents studied are identical general linear systems that aim at tracking a desired trajectory in presence of certain determinate disturbances. Under a mild assumption that the augmented communication topology has a spanning tree, a distributed control law based on relative output measurements between the agents and state measurements within the agent itself is proposed. It is shown that this output regulation problem can be solved if a Riccati equation with parameters has a positive definite symmetric solution. Moreover, by parameter determination of this Riccati equation, we find that the lower bound of the second smallest eigenvalue associated with the augmented graph Laplacian of the communication topology is of great importance on both the stability property and the convergence rate. A lower bound for this eigenvalue is given for N-node graphs.