This paper focuses on the prescribed-time cluster synchronization of coupled inertial neural networks. By variable transformation, the coupled inertial neural networks are converted into high-order systems. An effective prescribed-time control applicable to high-order systems is introduced by virtue of a time-varying scaling function. Moreover, a dimension-lifting approach is utilized to derive sufficient criteria for achieving prescribed-time cluster synchronization under the proposed control. Compared with existing Lyapunov–Krasovskii functional methods, the criteria obtained in this paper are in form of low-dimensional linear matrix inequalities and therefore can be easily verified. A numerical example is provided to demonstrate the effectiveness of proposed results.

This paper explores the synchronization of coupled inertial neural networks. By transforming the coupled INNs into partially coupled higher-order systems using variable transformation, sufficient criteria are derived for achieving the synchronization of coupled INNs by virtue of continuous and event-triggered pinning controls, respectively. In contrast to existing Lyapunov-Krasovskii functional techniques for analyzing coupled INNs, the approach adopted in this paper relies on Lyapunov function involving high-order systems, leading to more easily verifiable sufficient criteria. Two numerical illustrations are provided to demonstrate the validity of the obtained results.

This paper explores the projective synchronization of fuzzy inertial neural networks within predefined-time. An effective control strategy is proposed by means of a time-dependent scaling function. Sufficient criteria are derived rigorously for implementing the projective synchronization of fuzzy inertial neural networks within predefined-time. Particularly, when the projective coefficient is chosen as 1 or −1, the criteria of predefined-time complete and anti-synchronization of fuzzy inertial neural networks as a corollary are also provided. A numerical example is given to demonstrate the correctness of results in this paper.

This paper addresses the bipartite synchronization of coupled neural networks with time-varying delay. By introducing an effective quantized controller, the bipartite synchronization of coupled neural networks with time-varying delay is realized and sufficient conditions for assuring the bipartite synchronization are derived in virtue of a Halanay inequality. Moreover, the bipartite synchronization of coupled neural networks without delay via quantized controller is also taken into account in corollary as a special case. In the end, a numerical example is provided to demonstrate the correctness of theoretical results.

This article focuses on the tracking synchronization of the coupled non-identical neural networks. A kind of D-type iterative learning control (ILC) is proposed and the control input of each agent is updated iteratively such that tracking synchronization can be achieved under a repetitive environment. In addition, by virtue of the contraction mapping principle, some sufficient criteria for guaranteeing the tracking synchronization are established under the structurally fixed signed digraph. Finally, a numerical example is provided to demonstrate the viability of the theoretical results.