Disturbance attenuation of a network of nonlinear systems

This paper considers two problems related to disturbance attenuation in a network of nonlinear systems, in which each agent satisfies some suitable passivity properties and is subject to admissible disturbance in input: the interaction graph design and design of distributed controllers. We define a controlled output to measure the output disagreements among agents, and the two problems related to disturbance attenuation are converted to H-infinity suboptimal control problems. Under the assumption that the communication graph is connected and the edge weights are variables belonging to a convex set, we show that the disturbance attenuation performance can be enhanced by maximizing the second smallest eigenvalue of the graph Laplacian (when feedback gain is positive) or by minimizing the largest eigenvalue of the graph Laplacian (when feedback gain is negative). We provide some steps to obtain distributed controllers which achieve a prescribed performance under the assumption that the interaction graph is fixed. When there exist communication time-delays between the agents, we also consider two problems related to disturbance attenuation similar to the delay-free case. A numerical example about grounded capacitor RC circuit is presented to illustrate the effectiveness of the obtained results.