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In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means that the network synchronizes faster with lower-overshoot. The L2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L2 norm of the error vector e and the H2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H2 norm of the transfer function G is analyzed. Finally, an optimal controller is designed, according to the so-called LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L2 norm of the output of the linearized network.
The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can be measured
In this paper, the problem of pinning control for synchronization of complex dynamical networks is discussed. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramotos model in complex networks we determine patterns of meta-stability and calculate the modularity of the partition the
Network topology plays an important role in governing the collective dynamics. Partial synchronization (PaS) on regular networks with a few non-local links is explored. Different PaS patterns out of the symmetry breaking are observed for different wa
The IEEE 802.1 time-sensitive networking (TSN) standards aim at improving the real-time capabilities of standard Ethernet. TSN is widely recognized as the long-term replacement of proprietary technologies for industrial control systems. However, wire