Robust H_∞ controller design for dynamic consensus networks

This paper studies an H_∞ suboptimal control problems of consensus networks whereby the weights of network edges are no longer static gains, but instead are dynamic systems, leading to the notion of dynamic consensus networks. We apply model, orthogonal and diagonal transformations to a dynamic consensus network in order to reduce the overall system into N − 1 independent subsystems. We then establish a generalised methodology for designing a controller for a dynamic consensus network in the presence of external disturbances, focusing especially on using decentralised controllers that achieve consensus in the absence of disturbances and attenuation of disturbances to a prescribed H_∞ performance level. A design example is given to illustrate our results.