Scaled Consensus Tracking Under Constant Time Delay

Over the past decade, various schemes such as consensus, containment, and formation have been proposed for multi-agent systems. A multi-agent systems is said to have reached consensus when all the agents agree on a common value. Recently, however, scaled consensus was introduced as a new notion in the area of multi-agent systems. With this scheme, the agents reach different initial-state-dependent values. In this paper, the problem of scaled consensus tracking under constant time delay is addressed. Firstly, time delay is introduced to the tracking problem of scaled consensus. Then, a proper Lyapunov-Krasovskii functional is employed in order to study the stability of the system. In addition, it is shown that the maximum allowable time delay may be determined via the resultant LMIs. Finally, the findings of this paper are illustrated using a numerical example.