  The consensus control with optimal cost remains major challenging although
consensus control problems have been well studied in recent years. In this
paper, we study the consensus control of multi-agent system associated with a
given cost function. The main contribution is to present the distributed
control protocol while minimizing the given cost function with positive
semi-definite weighting matrix of control. The derived controller is composed
of two parts: One part is the feedback of the individual state which minimizes
the cost function and the other part is the feedback of the relative states
between the neighbours which guarantees the consensus. The presented results
are new to the best of our knowledge.
