Swarm stability for high-order linear time-invariant singular multi-agent systems

Abstract

Swarm-stability and swarm-stabilisation problems for high-order linear time-invariant singular multi-agent systems with directed networks are investigated. First, necessary and sufficient conditions for swarm stability and asymptotic swarm stability are proposed, which are independent of the dimensions of Jordan blocks of the Laplacian matrix of the interaction topology. Then, an approach is given to determine the absolute motion as a whole, and it is shown that the absolute motion is completely determined by initial states if the interaction topology is balanced. Furthermore, an approach is presented to determine gain matrices for asymptotic swarm stabilisation. Moreover, leader-following swarm-stability and swarm-stabilisation problems are investigated. Finally, numerical examples are given to demonstrate theoretical results.

Guaranteed Cost Consensus for Multi‐Agent Systems with Fixed Topologies

“…In the literature on consensus problems for multi-agent systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], the consensus regulation performance has been extensively investigated, while the energy consumption of the consensus control has not been considered simultaneously. By comparison with the aforementioned conclusions, the aim of the current paper is to obtain a tradeoff between the consensus regulation performance and the energy consumption.…”

“…Information consensus, which refers to a group of agents asymptotically reaching an agreement on a certain state of interest, is one of the fundamental problems of distributed coordination control for multi-agent systems. During the past few years, many works have addressed information consensus analysis and design problems for multi-agent systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…In [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], the consensus problems for multi-agent systems with various influence factors were investigated. Chen and Zhang [17] considered the interesting consensus problems for multi-agent systems with heterogeneous agents.…”

Guaranteed‐performance consensus tracking of singular multiagent systems with Lipschitz nonlinear dynamics and switching topologies

“…To remove these constraints, the equivalent sets technique is exploited to formulate our consensus conditions in terms of strict LMIs. (iv) Compared to the works of Xi et al 38 and Wu and Guan, 39 this paper gives an attempt to solve the guaranteed-performance consensus tracking problem for singular multiagent systems by considering the impacts of Lipschitz-type node dynamics and switching topologies. In addition, the derived results in this paper can be easily extended to solve the consensus tracking problem considered in the work of Wen et al 27 The rest of this paper is organized as follows.…”

Fuzzy distributed cooperative tracking for a swarm of unmanned aerial vehicles with heterogeneous goals

“…In Fax and Murray (2004), the authors focused on the stabilisation of a network of identical agents with linear dynamics whilst in Cai et al (2011) the authors suggested necessary and sufficient conditions for swarm stability of high-order linear time-invariant (LTI) multi-agent systems. Swarm-stabilisation problems for high-order LTI singular multi-agent systems with homogeneous agents was investigated in Xi et al (2013). A distributed output regulation approach for cooperative control of linear multi-agent systems in the presence of communication delays was subsequently presented in Yu and Wang (2014).…”