Global synchronization in finite time for fractional-order coupling complex dynamical networks with discontinuous dynamic nodes

The global Mittag-Leffler synchronization and global synchronization problem in finite time for fractional-order complex networks which with discontinuous nodes is studied in this paper. When the coupling matrix is time-varying and unknown, under the designed adaptive law with respect to the coupling matrix, by utilizing nonsmooth analysis method and Lyapunov functional approach as well as Laplace transform technique, the conditions of global Mittag-Leffler synchronization are achieved in terms of linear matrix inequalities (LMIs). When the coupling matrix is invariable and known, under the designed feedback controller, and by constructing a Lur'e Postnikov-type Lyapunov functional, the conditions of global synchronization in finite time are established, which are in the form of LMIs, and the upper bound of the settling time is explicitly evaluated. Finally, two examples are provided to illustrate the validity of the proposed design method and theoretical results. (C) 2019 Elsevier B.V. All rights reserved.