Containment analysis and design for high-order linear time-invariant singular swarm systems with time delays

Abstract

SUMMARY Containment analysis and design problems for high‐order linear time‐invariant singular swarm systems on directed graphs with time delays are investigated. To eliminate impulse terms in singular swarm systems and ensure that the singular swarm systems can achieve containment, time‐delayed protocols are presented for leaders and followers, respectively. By model transformation, containment problems of singular swarm systems are converted into stability problems of multiple low‐dimensional time‐delayed systems. In terms of linear matrix inequality, sufficient conditions are presented for time‐delayed singular swarm systems to achieve containment, which are independent of the number of agents. By using the method of changing variables, an approach is provided to determine the gain matrices in the protocols. Numerical simulations are shown to demonstrate theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Containment analysis and design for general linear multi-agent systems with time-varying delays

“…It is well-known that in practical applications, especially in practical networked systems, time-varying delays are inevitable due to that the communication bandwidth and the transmission rate are limited (see e.g., [29][30][31][32] and the references therein). However, time-varying delays were not considered in [21][22][23][24][25][26][27][28].…”

“…Li et al [22] proposed sufficient conditions for continuous-time and discretetime general high-order multi-agent systems to achieve state containment. Dong et al [23] investigated state containment problems for general high-order LTI singular multi-agent systems with constant time delays. Wen et al [24] studied robust containment problems for general multi-agent systems with uncertainties using a non-smooth control approach.…”

“…Secondly, the effects of time-varying delays on containment control of general high-order LTI multi-agent systems are considered in this paper. In [21][22][23][24][25][26][27][28], the dynamics of each agent is high-order but none of them considered time-varying delays. Thirdly, both sufficient conditions for general high-order multi-agent systems with time-varying delays to achieve containment and approaches to design the protocol are proposed.…”

Formation-containment control for high-order linear time-invariant multi-agent systems with time delays

“…Li et al [18] discussed containment problems for both continuous-time and discrete-time multi-agent systems with high-order linear time-invariant (LTI) dynamics. Dong et al [19] investigated containment problems for high-order LTI singular multi-agent systems with time delays. Containment problems for high-order multi-agent systems with parameter uncertainties were studied in [20,21].…”

“…In [22][23][24][25], there are not multiple leaders and only formation control problems were studied. Secondly, containment problems for multi-agent systems were discussed in [13][14][15][16][17][18][19][20][21], and it was assumed that leaders do not interact with each other to achieve timevarying formations. In this paper, leaders can interact with each other to achieve time-varying formations.…”