Impulsive adaptive pinning synchronization of Lur'e networks with cluster‐tree topology via parameters variation protocols

Abstract

This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time-varying delays and hybrid couplings. A novel impulsive adaptive pinning feedback control protocol is proposed with fully considering the cluster-tree topology structures of the networks and only imposed on the Lur'e systems in current cluster which exist directed paths with those Lur'e systems in the other clusters. In view of the concept of average impulsive interval, the comparison principle, the extended parameter variation methods, and the reductio ad absurdum, sufficient conditions are acquired for achieving the cluster synchronization of the derivative coupled Lur'e networks with considering different functions of the impulsive effects, respectively. Furthermore, according to the designed adaptive updating law, suitable feedback control strengths are obtained, which largely save the control costs. Finally, the effectiveness of the control schemes and the theoretical results have been proved by executing two numerical simulation examples.

Parameter variation‐based impulsive adaptive synchronization on Lur'e dynamical networks with hybrid time‐varying delays

“…Remark Till now, there are some linearization techniques for the nonlinear system function, such as Lipchitz condition, 12 the NCF condition, 13 the Sector condition 38 and so on. Among these techniques, Lipchitz condition is relatively strict but a widely applied one, for example in listed papers 12,18,26,27 …”

“…[6][7][8][9][10] Synchronization implies that the constituent systems in complex networks could present in the trend of convergence and finally reach to same states. According to prevailing control schemes and primary control targets, multiple kinds of synchronization patterns are investigated such as phase synchronization, 11 cluster synchronization, 12 impulsive synchronization 13 and adaptive synchronization. 14,15 Time delay, as one of the most quintessential and inevitable uncertainties, frequently occurs in practical fields like engineering, traffic and communication of information.…”

Iterative learning based convergence analysis for nonlinear impulsive differential inclusion systems with randomly varying trial lengths

“…In addition, the impulse is a sudden phenomenon generated by the interference of external complex environments, and many examples of this phenomenon can be found in real life (e.g., digital communication systems, growth of biological populations and treatment of infectious diseases). In recent decades, the research results of stability, controllability and optimal control theory for impulsive systems can be referred to References 28–32. Since the uncertain evolution of the systems may be affected by impulsive perturbations, more and more scholars have studied impulsive differential inclusion systems.…”