Bipartite Consensus for Multi-Agent Systems With Time-Varying Delays Based on Method of Delay Partitioning

Abstract

Bipartite consensus protocol is designed for multi-agent systems with time-varying delays. Then, the bipartite consensus problem is transformed into a corresponding stability problem by methods of gauge transformation and state transformation. The Lyapunov-Krasovskii functional is constructed, and the linear matrix inequality theory based on methods of delay partitioning and free matrix integral inequality is used to obtain sufficient conditions for a bipartite consensus of multi-agent systems. Both the first-order and second-order multi-agent systems are investigated. Finally, the effectiveness of the obtained results is illustrated by virtue of simulation results. INDEX TERMS Bipartite consensus, multi-agent systems, time-varying delays, delay partitioning, linear matrix inequality, free matrix integral inequality.

Tracking Control for General Second‐order Multi‐agent Systems with Communication Delay and Variable Topology

“…On the one hand, the time delay inevitably exists in reality due to signal transmission and algorithm processing. Many researchers have paid much attentions on the consensus problem with this constraint and there have been several papers, such as Wenying Hou et al studied consensus conditions for general second‐order multi‐agent systems with communication delay and deduce an explicit formula for the delay margin [17]; Middleton and Miller considered time delay margin for unstable plants using frequency domain analysis in reference [18]; reference [19] considered the containment control problem for second‐order multi‐agent systems with time‐varying delays and sufficient conditions to ensure containment control are given; reference [20] gave a sufficient condition for a class of double‐order multi‐agent systems to asymptotically achieve the bipartite consensus with the existence of communication delays; reference [21] presented necessary and sufficient conditions to guarantee consensus second‐order multi‐agent systems under a directed fixed topology in the presence of multiple constant delays, to cite just a few.…”

Delay-Induced Containment Control of Second-Order Multi-Agent Systems With Intermittent Sampled Position Data

“…In a multi-agent system, a group of autonomous agents asymptotically reach an agreement on certain quantities of interest by designing some distributed controllers based on the relative local information, which means that the consensus control is realized. For multi-agent systems, there have been many profound theoretical results on consensus [1]- [8].…”

“…t − τ ) = 0 if and only if the condition(8) holds. This completes the proof.Corollary Suppose that the communication topology graph G is undirected and connected.…”

Event-triggered consensus control for general second-order multi-agent systems

“…As an important basis of cooperative control, consensus is widely used in robot formation control, UAV task assignment, smart grid and so on. Therefore, great achievements have been obtained in the study of consensus problem Richert & Cortés, 2013;Sakurama & Ahn, 2019;Sun et al, 2020Sun et al, , 2019Zhang et al, 2019).…”