Distributed Weighted Average Tracking with Communication Delays

In this study, we explore the distributed weighted average tracking problem within a multi-agent system, considering the impact of communication delays. We begin by designing a control law tailored for distributed weighted average tracking under these delay conditions. Subsequently, we focus on scenarios with slow-varying delays and derive consensus conditions for the multi-agent system. These conditions are presented as linear matrix inequalities (LMIs), establishing a relationship between the control law parameters and delay values. Our findings reveal that the multi-agent system is capable of converging to the weighted average of the reference signals. We further substantiate our theoretical results with illustrative simulation examples.