Pinning control of complex Lur'e networks

This paper addresses the control problem of a class of complexdynamical networks with each node being a Lur'e system whosenonlinearity satisfies a sector condition, by applying localfeedback injections to a small fraction of the nodes. The pinningcontrol problem is reformulated in the framework of the absolutestability theory. It is shown that the global stability of thecontrolled network can be reduced to the test of a set of linearmatrix inequalities, which in turn guarantee the absolute stabilityof the corresponding Lur'e systems whose dimensions are the same asthat of a single node. A circle-type criterion in the frequencydomain is further presented for checking the stability of thecontrolled network graphically. Finally, a network of Chua'soscillators is provided as a simulation example to illustrate theeffectiveness of the theoretical results.