Recent Advance in Synchronization of Lur’e Dynamical Networks via Pinning Control

During the past two decades, it has been witnessed that the studies on complex dynamical networks are subjected to much ongoing investigations because of its deeply potential applications not only in real-word systems like the fields of medical treatments, transportation networks, smart grid, but also in artificial networks like the fields of coauthor index, social communication networks. As a remarkable coordination behavior in complex dynamical networks, state synchronization has drawn lots of attention from all over the world, and it covers many subjects, such as physics, applied mathematics, social science, statistics, computer science and so on. In fact, synchronization of a complex network denotes regulating all/part of the systems in the networks in order to force them to perform consistently. Different synchronization patterns have been widely studied, such as the generalized synchronization, lag synchronization, cluster synchronization, finite-time synchronization, robust synchronization and so on. However, it is impossible and even cost much to impose the controllers to every nodes for controlling the network with large number of nodes in reality. Thus, the pinning control with minor part of nodes are picked to be controlled is introduced, and has been widely utilized for its practical convenience and better performance.