The time-triggered impulsive control of complex homogeneous dynamical networks has received wide attention due to its occasional occupation of the communication channels. This article is devoted to quasisynchronization of heterogeneous dynamical networks via event-triggered impulsive controls with less channel occupation. Two kinds of triggered mechanisms, that is, the centralized event-triggered mechanism in which the control is updated based upon the state information of all nodes, and the distributed event-triggered mechanism where the control is updated according to the state information of each node and its neighboring node, are proposed, respectively, such that the synchronization error between the heterogeneous dynamical networks and a virtual target is not more than a nonzero bound. What is more, the Zeno behavior is shown to be excluded. It is found that the combination method of the event-triggered control and the impulsive control, that is, the distributed event-triggered impulsive control has the advantage of low-energy consumption and takes up many fewer communication channels over the time-triggered impulsive control. Two numerical examples are conducted to illustrate the effectiveness of the proposed event-triggered impulsive controls.

The time-triggered impulsive controls were widely used to study the collective behavior of homogeneous dynamical networks due to their low control cost, which was a bit conservative in the occupation of communication channels. This article addresses designing the event-triggered impulsive controls for the quasisynchronization, namely, a weak cooperative behavior with the synchronization error no more than a positive constant in the leader-following heterogeneous dynamical network, which thus can reduce the occupation of resources significantly. The centralized and distributed impulsive controls are designed to lead the followers to synchronize approximately to the leader within a nonzero bound, where the impulsive instants are triggered, respectively, by the global or local state-dependent conditions. Numerical results are put forward to verify the effectiveness of the proposed methods.

This paper is primarily devoted to the predefinedtime average consensus of heterogeneous nonlinear leaderless multi-agent systems(MASs). Firstly, the predefined-time stability for a class of fixed-time stable systems is studied, which greatly improves the overestimation for the settling time of the fixed-time stability. Moreover, compared with the classical conclusions, our results are more suitable for the control of nonlinear MASs. Then, on the basis of the proposed stability analysis, a simple control algorithm is designed for ensuring the predefined-time average consensus of the system under consideration. With this predefined-time approach, any desired settling time can be achieved by adjusting the control gain. Finally, numerical simulation is shown to support the theoretical analysis.

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

The cooperation of linear multiagent systems (MASs) in the signed graphs has received wide attention. However, time delays and nonlinearity are ignored. This article deals with the cooperation behavior, especially interval bipartite synchronization (IBS) of delayed nonlinear neural networks (NNs) with signed graphs. A generalized matrix is proposed for the construction of the Lyapunov functionals, establishing sufficient conditions in a linear matrix inequality related to the coupling strength, the delays, and the network structure. It suggests that the negative rooted cycles and the negative nonrooted cycles take an important part in stabilizing delayed nonlinear NNs and leading to their diversity, and time delays, especially communication delays, significantly impact cooperation performance. Numerical examples are employed to validate our derived results.