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This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances.A dynamical network is said to be robust to disturbance,if the H ∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small.It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H ∞ control problem of a set of independent systems whose dimensions are equal to that of a single node.A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node.To improve this,local feedback injections are applied to a small fraction of the nodes in the network.Some criteria for possible performance improvement are derived in terms of linear matrix inequalities.It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees. 相似文献
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This paper addresses the control problem of a class of complex
dynamical networks with each node being a Lur'e system whose
nonlinearity satisfies a sector condition, by applying local
feedback injections to a small fraction of the nodes. The pinning
control problem is reformulated in the framework of the absolute
stability theory. It is shown that the global stability of the
controlled network can be reduced to the test of a set of linear
matrix inequalities, which in turn guarantee the absolute stability
of the corresponding Lur'e systems whose dimensions are the same as
that of a single node. A circle-type criterion in the frequency
domain is further presented for checking the stability of the
controlled network graphically. Finally, a network of Chua's
oscillators is provided as a simulation example to illustrate the
effectiveness of the theoretical results. 相似文献
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