On the synthesis ofH∞consensus for multi-agent systems

This paper studies the H∞ consensus problem of multi-agent systems by means of a simultaneous stabilization approach. It is shown that the H∞ consensus design problem for n coupled agents can be equivalently characterized as a problem of the simultaneous H∞ stabilization of n − 1 independent subsystems. A new consensus analysis condition is obtained by investigating the corresponding simultaneous H∞ stabilization problem. Based upon the analysis condition, a necessary and sufficient condition is derived to guarantee the consensus of multi-agent systems with a prescribed H∞ performance, where the controller gain matrix is not coupled with the Lyapunov matrices, but parametrized by a positive-definite matrix. Iterative convex optimization approaches are further developed to solve the synthesis condition and to choose the initial values. Finally, a numerical example is given to show the applicability of the results.