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Summary: In this article, the global and exponential synchronization of Lur'e networks with hybrid time‐varying delays is investigated. For sake of saving control costs, a novel impulsive adaptive controller is presented, where the adaptive feedback control input is utilized to compensate the control effects of the impulsive signal. Meanwhile, suitable control gains are obtained according to the designing on adaptive updating laws. In view of the definition of average impulsive interval, the generalized comparison principle and the formula of parameter variation, sufficient conditions for achieving global and exponential synchronization of Lur'e dynamical networks are eventually derived. Two relevant numerical simulations are provided to illustrate the effectiveness of theoretical analysis and the control scheme. [ABSTRACT FROM AUTHOR]

Summary: 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. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential synchronization of coupled Lur’e dynamical networks with multiple time-varying delays and derivative coupling. In order to synchronize the Lur’e dynamical networks to the corresponding Lur’e systems, we propose a kind of impulsive pinning control strategy, where different functions of impulsive effects are taken into account. Sufficient conditions are derived for the exponential synchronization of the derivative coupled Lur’e dynamical networks by jointly applying the contradiction proof method, the concept of an average impulsive interval, comparison principle, and the extended parameters variation formula. Simultaneously, the convergence rates of exponential synchronization are obtained according to the definition of the impulsive solution equation on different functions of impulsive effects. Furthermore, three numerical examples are presented to demonstrate the validity of the theoretical analysis and the control protocol. [ABSTRACT FROM AUTHOR]