Scaled consensus of multi-agent systems under time-varying delay

In recent years, multi-agent systems have drawn a lot of attention. Consensus problem of these systems has been extensively studied in the past decade. However, in a recent paper, the concept of scaled consensus was introduced. Unlike conventional consensus, agents reach different initial-state-dependent values. On the other hand, time delay is an important issue in networks of agents; hence, this paper introduces time-varying delay to the scaled consensus problem. Moreover, a Lyapunov-Krasovskii approach is adopted to check the stability of the system. The allowable delay value is computed using the resultant LMIs. In order to validate our findings, a numerical example is provided.