Limits...
Consensus of Nonlinear Complex Systems with Edge Betweenness Centrality Measure under Time-Varying Sampled-Data Protocol.

Park MJ, Kwon OM, Cha EJ - ScientificWorldJournal (2015)

Bottom Line: This paper proposes a new consensus criterion for nonlinear complex systems with edge betweenness centrality measure.By construction of a suitable Lyapunov-Krasovskii functional, the consensus criterion for such systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms.One numerical example is given to illustrate the effectiveness of the proposed methods.

View Article: PubMed Central - PubMed

Affiliation: School of Electrical Engineering, Chungbuk National University, 52 Naesudong-ro, Cheongju 361-763, Republic of Korea.

ABSTRACT
This paper proposes a new consensus criterion for nonlinear complex systems with edge betweenness centrality measure. By construction of a suitable Lyapunov-Krasovskii functional, the consensus criterion for such systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed methods.

No MeSH data available.


Results without the consensus protocol, that is, ui(tk) = 0: (a) phase and (b) each state.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4489014&req=5

fig7: Results without the consensus protocol, that is, ui(tk) = 0: (a) phase and (b) each state.

Mentions: However, the system performance with the edge betweenness centrality measure is more poor and needs more protocol input than the one with the degree centrality measure. For comparison between two measure cases, the sampling interval tk+1 − tk (=hM) is assumed to be 0.4. Figure 4 shows that the states with the responses consent to the same behavior under two measure cases for the given initial states of the nodes x1T(0) = [0.1  0.5–0.7] and x2T(0) = [3  1–4]. In Figure 5, their error trajectories are shown. Here, the case of the edge betweenness centrality measure indicates the poor performance. Thus, it can be confirmed that it is necessary to consider the global information for network structure as mentioned in Remark 1. Their corresponding protocol inputs can be identified in Figure 6. In addition to this, without the protocol, the behaviors of two nodes are different as shown in Figure 7.


Consensus of Nonlinear Complex Systems with Edge Betweenness Centrality Measure under Time-Varying Sampled-Data Protocol.

Park MJ, Kwon OM, Cha EJ - ScientificWorldJournal (2015)

Results without the consensus protocol, that is, ui(tk) = 0: (a) phase and (b) each state.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4489014&req=5

fig7: Results without the consensus protocol, that is, ui(tk) = 0: (a) phase and (b) each state.
Mentions: However, the system performance with the edge betweenness centrality measure is more poor and needs more protocol input than the one with the degree centrality measure. For comparison between two measure cases, the sampling interval tk+1 − tk (=hM) is assumed to be 0.4. Figure 4 shows that the states with the responses consent to the same behavior under two measure cases for the given initial states of the nodes x1T(0) = [0.1  0.5–0.7] and x2T(0) = [3  1–4]. In Figure 5, their error trajectories are shown. Here, the case of the edge betweenness centrality measure indicates the poor performance. Thus, it can be confirmed that it is necessary to consider the global information for network structure as mentioned in Remark 1. Their corresponding protocol inputs can be identified in Figure 6. In addition to this, without the protocol, the behaviors of two nodes are different as shown in Figure 7.

Bottom Line: This paper proposes a new consensus criterion for nonlinear complex systems with edge betweenness centrality measure.By construction of a suitable Lyapunov-Krasovskii functional, the consensus criterion for such systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms.One numerical example is given to illustrate the effectiveness of the proposed methods.

View Article: PubMed Central - PubMed

Affiliation: School of Electrical Engineering, Chungbuk National University, 52 Naesudong-ro, Cheongju 361-763, Republic of Korea.

ABSTRACT
This paper proposes a new consensus criterion for nonlinear complex systems with edge betweenness centrality measure. By construction of a suitable Lyapunov-Krasovskii functional, the consensus criterion for such systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed methods.

No MeSH data available.