Global stabilisation of Lur'e network
Zengqiang Chen, Linying Xiang, Guan Ron Chen, Zhongxin Liu, Zhuzhi Yuan · International Journal of Systems Control and Communications · 2009
A new complex dynamical network model consisting of Lur'e systems are proposed and studied in this paper. Some new global stabilisation conditions are derived based on the Lyapunov stability theory, which guarantee that the whole network can be pinned to its equilibrium by placing some feedback controllers on a small fraction of nodes. In some particular cases, even a single controller can achieve the control objective. It is found that global stabilisation of such a network is completely determined by the dynamics of each individual node, the coupling strength, the inner-coupling matrix, and the eigenvalues of the coupling matrix as well as the feedback-gain matrix of the network.