Projective synchronization of a class of complex network based on high-order sliding mode control

Robust fixed‐time synchronisation of non‐identical nodes in complex networks under input non‐linearities

“…In the synchronisation problem, nodes interconnected to the network should be reached a common state, when the network evolves. So far, different types of synchronisation, such as quasi synchronisation [3], phase synchronisation [4], complete synchronisation [5], and cluster synchronization [6], including different coupling of nodes and topologies have been investigated by using different control strategies such as state feedback control [7][8][9], output feedback control [10,11], impulsive control [12,13], intermittent control [14,15], pinning control [16,17], adaptive control [18,19], and sliding mode control [20][21][22][23]. Nevertheless, in these works, Lyapunov stability of the synchronisation process is just ensured.…”

Sliding mode synchronization of a delayed complex dynamical network in the presence of uncertainties and external disturbances

“…On the other hand, sliding mode control can attenuate the impact of uncertainties effectively with less information and computational burden in comparison with adaptive controllers. Therefore, some papers considered the sliding mode control for synchronizing the CDNs (Chen et al, 2017; Hou et al, 2016; Liu and Chen, 2015; Lü et al, 2013; Sun et al, 2015). A second-order terminal sliding mode controller is designed for outer synchronization of a class of complex networks with disturbances in Liu and Chen (2015).…”

Exponential synchronization of fractional-order complex networks via pinning impulsive control

“…There were some kinds of synchronization have been investigated, such as lag synchronization, which requires the states of response system to synchronize with the past states of the drive system [12]. The situation that the driver and response systems could be synchronized up to a scaling function is named projective synchronization [13]. When a network can be divided into some groups, and coupled nodes in the same cluster can be synchronized, but there is no synchronization among different clusters, the network is said to realize the cluster synchronization [14].…”