TY - GEN

T1 - Mean square stability of consensus over fading networks with nonhomogeneous communication delays

AU - Wang, Jing

AU - Elia, Nicola

PY - 2008

Y1 - 2008

N2 - In this paper, we propose a discrete time consensus protocol which can solve the consensus problem in the network with nonhomogeneous communication delays. We give the sufficient conditions to reach consensus and provide a closed form formula for the consensus value. Furthermore, we investigate the mean square stability (MSS) of our protocol when each link of the network can break with a given probability at each time interval. The condition for checking MSS is equivalent to checking the spectral radius of a positive matrix. To gain more insight, we further restrict our attention to spatially invariant network structure and develop a more efficient expression to check the MSS. We derive a closed form formula to determine the MSS in the limit of large delays, get useful lower and upper bounds and analyze their implications for large classes of network topologies. We find that the consensus protocol is robust to link failures in the sense the system is always mean square stable if we put restrictions on the propagation gain.

AB - In this paper, we propose a discrete time consensus protocol which can solve the consensus problem in the network with nonhomogeneous communication delays. We give the sufficient conditions to reach consensus and provide a closed form formula for the consensus value. Furthermore, we investigate the mean square stability (MSS) of our protocol when each link of the network can break with a given probability at each time interval. The condition for checking MSS is equivalent to checking the spectral radius of a positive matrix. To gain more insight, we further restrict our attention to spatially invariant network structure and develop a more efficient expression to check the MSS. We derive a closed form formula to determine the MSS in the limit of large delays, get useful lower and upper bounds and analyze their implications for large classes of network topologies. We find that the consensus protocol is robust to link failures in the sense the system is always mean square stable if we put restrictions on the propagation gain.

KW - Mean-square stability robustness

KW - Network consensus

KW - Spatially invariant systems

UR - http://www.scopus.com/inward/record.url?scp=62949246831&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62949246831&partnerID=8YFLogxK

U2 - 10.1109/CDC.2008.4739345

DO - 10.1109/CDC.2008.4739345

M3 - Conference contribution

AN - SCOPUS:62949246831

SN - 9781424431243

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4614

EP - 4619

BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 47th IEEE Conference on Decision and Control, CDC 2008

Y2 - 9 December 2008 through 11 December 2008

ER -