Allowable delay bound for consensus of linear multi-agent systems with communication delay

Finding the exact delay bound for consensus of linear multi-agent systems

“…The adjacency matrix of this topology is given by: and its corresponding Laplacian matrix has three different eigenvalues: 0, 1.3820 and 3.6180, the last two of them have multiplicity equal to two. We use the same 1 feedback gain reported by [32]:…”

“…Most of the works mentioned study systems with very simple dynamics. On the contrary, [32] is one of the few works that address the problem of state consensus on networks of agents driven by higher-order, general linear dynamics under undirected communications and affected by constant time delays. By transforming the consensus problem into a robust stability problem for an uncertain system, they arrive to an allowable delay bound for systems with fixed and switching interconnection topologies.…”

“…We show that this methodology provides exact stability bounds in the domain of the delay, and its deployment is straight forward. We compare our results to those of [32] to show the advantages of our method.…”

Sliding mode control for multi-agent systems under a time-varying topology

“…Especially, consensus and tracking problems for multi-agent systems has been intensively investigated (Cui & Jia, 2012;Du, Li, & Shi, 2012;Hong, Hu, & Gao, 2006;Hu, 2010;Park, Lee, Son, Kwon, & Cha, 2013;Qin, Gao, & Zheng, 2011;Shen, Jiang, Shi, & Zhao, 2013;Sun & Guan, 2013;Xie, Liu, Wang, & Jia, 2009;Xie & Wang, 2012;Yu, Chen, Cao, & Kurths, 2010;Zhang & Tian, 2013). Specifically, Zhang and Tian (2013), studies the consensus problem of multi-agent systems with multiple time delays and Shen et al (2013), proposes a fuzzy tracking control scheme which can minimise the time delay due to fault diagnosis and reduce the adverse effect on tracking performance. A non-smooth backstepping controller is designed to deal with the robust consensus problem for multi-agent systems with external disturbances in Du et al (2012).…”

Delayed-Compensation Algorithm for Second-Order Leader-Following Consensus Seeking under Communication Delay

“…Convergence of synchronously-coupled consensus algorithm depends on communication delay strictly for multi-agent systems under fixed [1][2][3][4][5] or switched topologies [6][7][8][9][10][11][12][13]. To our great delight, the first-order and second-order agents with stationary consensus algorithms in the asynchronously-coupled form can be robust to arbitrary communication delays by choosing proper control parameters [14][15][16][17][18][19][20][21][22].…”