Robust Output Feedback Consensus for Networked Negative-Imaginary Systems

Abstract

A robust output feedback consensus problem for networked homogeneous negative-imaginary (NI) systems is investigated in this technical note. By virtue of NI systems theory, a set of reasonable yet elegant conditions are derived for output consensus under ${\Fraktur{L}}_{2}$ external disturbances as well as NI model uncertainty. As a byproduct, this technical note also reaffirms a previous result by Li et al. which shows the robustness of networked systems is always worse than that of single agent systems. Furthermore, the eventual convergence sets are also characterized for several special NI systems that are commonly studied in the literature. It is shown how the results in this work embed and generalize earlier results for these classes of systems. We show that the natural convergence set boils down to the centroid of the initial pattern when the initial conditions of the controllers are zero. Numerical examples are given to showcase the main results.