TY - JOUR
T1 - Dynamic Feedback Synchronization of Lur'e Networks via Incremental Sector Boundedness
AU - Zhang, Fan
AU - Trentelman, Harry L.
AU - Scherpen, Jacquelien M. A.
PY - 2016/9
Y1 - 2016/9
N2 - In this note, we generalize our results on synchronization of homogeneous Lur'e networks by static, relative state information based protocols from Zhang et al to the case that for each agent only relative measurements are available. We establish sufficient conditions under which a linear dynamic synchronization protocol exists for such networks. These conditions involve feasibility of two LMI's together with a coupling inequality, reminiscent of the well-known LMI conditions in H∞ control by measurement feedback. We show that, regardless of the number of agents in the network, only the three inequalities are involved. In the computation of the protocol matrices, the eigenvalues of the Laplacian matrix of the interconnection graph occur. In particular, the matrices representing the protocol depend on the smallest nonzero eigenvalue and the largest eigenvalue of the Laplacian matrix. We validate our results by means of a numerical simulation example.
AB - In this note, we generalize our results on synchronization of homogeneous Lur'e networks by static, relative state information based protocols from Zhang et al to the case that for each agent only relative measurements are available. We establish sufficient conditions under which a linear dynamic synchronization protocol exists for such networks. These conditions involve feasibility of two LMI's together with a coupling inequality, reminiscent of the well-known LMI conditions in H∞ control by measurement feedback. We show that, regardless of the number of agents in the network, only the three inequalities are involved. In the computation of the protocol matrices, the eigenvalues of the Laplacian matrix of the interconnection graph occur. In particular, the matrices representing the protocol depend on the smallest nonzero eigenvalue and the largest eigenvalue of the Laplacian matrix. We validate our results by means of a numerical simulation example.
KW - Incremental sector boundedness
KW - linear matrix inequalities
KW - Lur'e system
KW - synchronization
KW - ROBUST SYNCHRONIZATION
KW - SYSTEMS
KW - NONLINEARITIES
KW - CONSENSUS
UR - http://www.scopus.com/inward/record.url?scp=84985991862&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84985991862&origin=recordpage
U2 - 10.1109/TAC.2015.2494840
DO - 10.1109/TAC.2015.2494840
M3 - 21_Publication in refereed journal
VL - 61
SP - 2579
EP - 2584
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 9
ER -