Bounded synchronisation of singularly perturbed complex network with an application to power systems

Abstract

This study is concerned with the bounded synchronisation of singularly perturbed complex network. If the reduced network is boundedly synchronised, the authors obtain, by using partially contracting theory, an explicit bound for small perturbation parameter to guarantee the bounded synchronisation of singularly perturbed complex network. Moreover, the authors present a sufficient condition such that the reduced network is boundedly synchronised. Although this sufficient condition is difficult to test directly for general networks, it can be tested for power networks based on some existing results. The effectiveness of the proposed results is demonstrated via power networks.

Synchronization Control for a Class of Discrete-Time Dynamical Networks With Packet Dropouts: A Coding–Decoding-Based Approach

“…For presentation convenience, only some cases of packet dropouts for the dynamical network are described in (43). Specifically, without loss of generality, we assume that the first m nodes suffer from the packet dropouts where m ∈ {1, 2, .…”

“…Roughly speaking, the synchronization phenomenon means that the state trajectories of all nodes tend to a certain identical value asymptotically. Recently, the synchronization problem for dynamical networks has attracted considerable research attention as evidenced by practical applications in a diverse range of areas such as the synchronization of sampling frequency in the industrial applications of wireless sensor networks [3], the phase synchronization of power networks [10], [43], the synchronization of memristor-based dynamical networks [13], and the global synchronization of public traffic road networks [1], to name just a few. However, in reality, there may be a case that the synchronization phenomenon cannot be attained for autonomous networks by their local connections, that is, the dynamic evolutions exhibit the asynchronous nature.…”

Finite-Time Bounded Synchronization of the Growing Complex Network with Nondelayed and Delayed Coupling

“…In addition, as bounded control of complex system is relevant in practical applications, for example, power networks cannot achieve complete synchronization, so it is desirable to obtain conditions within given bound such that the rotor phase differences between the generators remain [16]. In recent years, bounded control of complex dynamical network concerns the existence of bounded synchronization region globally stabilizing the complex system, which has grown very quickly, and it is one of the important issues in control theory and applications [17][18][19][20][21].…”

“…In [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], the authors studied the numbers of the nodes in the networks invariant about synchronization of complex dynamical networks. As the structures of many complex systems are typically dynamic, some new nodes can enter the network as time goes on [22].…”

Synchronization for singularity-perturbed complex networks via event-triggered impulsive control

“…These kinds of systems can be modeled as singularity-perturbed complex networks (SPCNs), where a small and positive singular perturbation parameter (SPP) ε is introduced to describe the two-timescale characteristic [2,22,26]. Moreover, the synchronization problem of SPCNs has received considerable attention due to its wide applications in biological systems, neuronal networks and electric power systems [3,6,28,35].…”