Abstract
This paper deals with distributed control for a class of multi-agent systems composed of a lot of interconnected agents each of which has the first order dynamics. It is assumed that the interconnection can be described as an undirected graph. Then, a necessary and sufficient condition for stability of the closed-loop system is presented in terms of the distributed feedback gains. A sufficient condition for optimality of the system is further presented, where it is shown that the distributed feedback can minimize a quadratic performance index if a gain is selected sufficiently large. The results are also extended to the case that each of the agents has a higher order dynamics.
