Abstract
A complex earthquake monitor network includes satellite in-orbit and ground observation and requires good synchronization in time. This article investigates synchronization of complex networks with uncertainty and time-delay. Directed graphs are used to represent the interaction topology. The uncertainty is assumed to be norm bounded. Based on Lyapunov theory, sufficient conditions are given to guarantee the synchronization of the complex networks in the presence of time-delay. Simulation results are provided to demonstrate the effectiveness of the obtained results.
Highlights
A complex network consists of a large number of interconnected nodes, in which each node is a fundamental unit with specific purpose, especially when the earthquake monitor network covers types of observation instruments
Some information in a complex network may not be able to be transmitted completely precisely due to the existence of various disturbances, such as uncertainty, time-delay, and the variation of the network topology,[14,15,16,17,18,19] which might lead to divergence or oscillation of the complex networks
International Journal of Distributed Sensor Networks absence and presence of time-delay, it is shown that all nodes can reach synchronization with desired H‘ performance even when the external disturbances and the parameter uncertainties coexist
Summary
Synchronization of complex dynamical networks have attracted considerable attention from so many fields such as biology, physics, robotics, and control engineering.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] This is partly due to recent technological advances in communication and computation, and important practical applications, ranging from the Internet, automated highway systems, low-orbit satellites, coordinated navigation, multi-sensor of earthquake monitoring network,and so on.[23,24,25,26] A complex network consists of a large number of interconnected nodes, in which each node is a fundamental unit with specific purpose, especially when the earthquake monitor network covers types of observation instruments. Few works have been conducted to consider the parameter uncertainties and time-delay simultaneously for general complex networks. International Journal of Distributed Sensor Networks absence and presence of time-delay, it is shown that all nodes can reach synchronization with desired H‘ performance even when the external disturbances and the parameter uncertainties coexist. The directed graph G has a spanning tree if and only if Laplacian L of G has a simple zero eigenvalue (with associated eigenvector 1n)[12]. According to Lemma 2, DL can be decomposed into DL = E1S(t)E2, where E1, E2 are specified constant matrices and S(t) is a diagonal matrix, whose diagonal elements are the uncertainties of the edges, that is, the non-zero DLij(t) s. We address the global synchronization of network and give design rules of the Laplacian L in the presence of time-delay and uncertainty.
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