Distributed H∞ constrained consensus problem

This paper is concerned with the distributed H∞ constrained consensus problem for multi-agent systems. The objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired H∞ performance index in the presence of external disturbances. A nonlinear distributed algorithm is adopted to solve this constrained consensus problem. To measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set, a nonlinear function is constructed as the H∞ output function. By analyzing the convexity of the convex set, a sufficient condition is given to solve the constrained consensus problem with the desired H∞ performance. Finally, a numerical simulation example is provided to show the effectiveness of our theoretical results.