Graph partitions and the controllability of directed signed networks

Liu, Xianzhu; Ji, Zhijian; Hou, Tao

doi:10.1007/s11432-018-9450-8

Cited by 25 publications

(9 citation statements)

References 42 publications

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“…e k-kernels of a graph play a key role in describing the structures of graphs and have a wide application prospect in the network systems [29]. A subset S of nodes of a graph G is called a k-kernel if S is both a k-ESS and a k-internally stable set (k-ISS) of G. Yue and Yan [24] considered the algebraic formulation of k-ISS of graphs in the framework of STP and proposed the matrix form of the necessary and sufficient condition of k-ISS.…”

Section: Further Results On K-kernelsmentioning

confidence: 99%

Matrix Approach to Formulate and Search k-ESS of Graphs Using the STP Theory

Yue

Yan

Deng

2021

Journal of Mathematics

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In this paper, the structure of graphs in terms of k-externally stable set (k-ESS) is investigated by a matrix method based on a new matrix product, called semitensor product of matrices. By defining an eigenvector and an eigenvalue of the node subset of a graph, three necessary and sufficient conditions of k-ESS, minimum k-ESS, and k-kernels of graphs are proposed in a matrix form, respectively. Using these conditions, the concepts of k-ESS matrix, minimum k-ESS matrix, and k-kernel matrix are introduced. These matrices provide complete information of the corresponding structures of a graph. Further, three algorithms are designed, respectively, to find all these three structures of a graph by conducting a series of matrix operation. Finally, the correctness and effectiveness of the results are checked by studying an example. The proposed method and results may offer a new way to investigate the problems related to graph structures in the field of network systems.

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Section: Further Results On K-kernelsmentioning

confidence: 99%

Matrix Approach to Formulate and Search k-ESS of Graphs Using the STP Theory

Yue

Yan

Deng

2021

Journal of Mathematics

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“…(38) Theorem 3. Under Assumption 1, the multiagent systems (3) with protocol (35) can track system (2) successfully under the event-triggering condition (36), where K � B T P and W � PBB T P.…”

Section: Decentralized Event-triggered Control Strategymentioning

confidence: 99%

“…Also its distributed cooperative control [1,2] has attracted more and more researchers' attention. For example, the controllability [3][4][5][6][7][8][9][10][11] and the consensus problem [12][13][14][15][16][17][18][19] are widely studied in multi-agent systems. Among them, as the basic problem of multi-agent cooperative control, consensus is widely used in formation control [20], cluster control, sensor network and other aspects, which is a research hot issue in the control discipline at present.…”

Section: Introductionmentioning

confidence: 99%

Event-Based Consensus for General Linear Multiagent Systems under Switching Topologies

Sun

Liu

2020

Complexity

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In this paper, event-triggered leader-following consensus of general linear multiagent systems under both fixed topology and switching topologies is studied. First, centralised and decentralised event-triggered control strategies based on neighbors' state estimation are proposed under fixed topology, in which the controller is only updated at the time of triggering. Obviously, compared with the continuous time control algorithms, the event-triggered control strategies can reduce the communication frequency among agents effectively. Meanwhile, event-triggering conditions are derived for systems to achieve consensus by using the Lyapunov stability theory and model transformation method. en, the theoretical results obtained under the fixed topology are extended to the switching topologies, and the sufficient conditions for the system to achieve leader-following consensus under the switching topologies are given. However, different from fixed topology, the control input of each agent is updated both at event-triggering and topology switching time. Finally, Zeno behaviors can be excluded by proving that the minimum triggering interval of each agent is strictly positive, and the effectiveness of the event-triggered protocol is verified by simulation experiments.

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“…The problems of cooperative control for multi-agent systems have been concerned widely by researchers at home and abroad because of its important significance both in theory and reality. For example, the consensus [1]- [6] and controllability [7]- [16] have been widely studied for multi-agent system. As a basic problem of cooperative control, the research on consensus of multi-agent systems is always a hot topic.…”

Section: Introductionmentioning

confidence: 99%

Bipartite Consensus of Multi-Agent Systems With Intermittent Interaction

Sun¹,

Ji²,

Qi³

et al. 2019

IEEE Access

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This paper studies the bipartite consensus problem of multi-agent systems with intermittent interaction under signed directed graph. It is assumed that each agent receives its states information relative to its neighbors at the sampling time and updates the control input by using the states information, and the period of each agent updates control input is equal to a positive integer multiple of its sampling period. Cooperation and competition between agents are represented by positive and negative weights of edge respectively in the signed topology. The sufficient condition for achieving bipartite consensus is obtained by Shure-Cohen stability criterion, which reveals the relationship among sampling period, update control input period and controller gain of system. Finally, simulation tests show the bipartite consensus performances of agents under intermittent protocol and signed topology.INDEX TERMS Multi-agent systems, intermittent interaction, bipartite consensus, positive and negative weights, Shure-Cohen stability criterion.

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Graph partitions and the controllability of directed signed networks

Cited by 25 publications

References 42 publications

Matrix Approach to Formulate and Search k-ESS of Graphs Using the STP Theory

Matrix Approach to Formulate and Search k-ESS of Graphs Using the STP Theory

Event-Based Consensus for General Linear Multiagent Systems under Switching Topologies

Bipartite Consensus of Multi-Agent Systems With Intermittent Interaction

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