# Quasi-Consensus of Disturbed Nonlinear Multiagent Systems with Event-Triggered Impulsive Control
###### Abstract  
Considering the external disturbances, in this paper, the quasi-consensus of multiagent systems is studied via event-triggered impulsive control. By designing a novel event-triggered mechanism (ETM), sufficient conditions to realize leader-following quasi-consensus are derived with event-triggered impulsive control. Additionally, Zeno behavior is also excluded. It is shown that the event-triggered frequency is closely related to the parameters selected in the designed ETM, and less conservative results can be obtained compared with the existing results. Finally, a simulation example is given to demonstrate the effectiveness of our proposed results. external disturbances; leader-following quasi-consensus; event-triggered impulsive control; Zeno behavior +
Footnote †: journal: Applied  
1
Footnote 1: _Applied_  
22 July 2022  
**Published:** 28 July 2022  
**Published:** maps and institutional affiliations. **Published:** 28 July 2022  
**Published:** **Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Considering the communication load and control cost, the selection and design of control strategy are very important in the research on the consensus of MASs. At the beginning, scholars used continuous control to make the MASs realize consensus, such as including control [18], adaptive control [19], pinning control [20], etc. Although continuous control is relatively simple, continuous control requires the controller to work all the time, which leads to a waste of resources. To solve this problem, scholars proposed impulsive control, but the impulsive sequence is generally set and selected manually in advance. Impulsive control has been widely used in the control field because of its low control cost, strong robustness and good confidentiality. For examples, using impulsive control method, [PERSON] [21] studied the stabilization of delayed systems; [PERSON] [22] investigated the synchronization of delayed neural networks; and [PERSON] [23] considered the consensus of delayed MASs with random disturbances. However, because the impulsive sequence is artificially set, it may be too conservative a lead to increase unnecessary control times. To solve these shortcoming, the event-triggered mechanism (ETM) [24; 25; 26; 27] was proposed. The control sequence depends on some triggering conditions according to the system state and so on. Compared with time-triggered impulsive control, event-triggered impulsive control (ETIC) combines both the event-triggered strategy and impulsive control, and hence, ETIC can effectively reduces the cost of control [28; 29; 30; 31]. At present, scholars attach great importance to the research of ETIC strategy. For instant, using ETIC, the consensus of linear MASs [28], synchronization of neural networks [30] and complex dynamic networks [29] were investigated. Inspired by the above discussion, based on the ETIC strategy, this paper studies the quasi-consensus of nonlinear MASs with various obstructions (ROUs, RONs and external disturbances). The main contributions are as follows:  
* In this paper, various obstructions are considered. Compared with the works in [31], the stochastic characteristics of uncertainties, i.e., ROUs and RONs, are considered. Moreover, the external disturbances in the leader and followers here can be different. Hence, the system model is more general and practical. * The ETM designed in this paper is antidisturbance compared with the existing results [32; 33; 34]. Additionally, differently from the one in [31], the effects of disturbances are intuitive, which makes it easier to adjust for various disturbances. **Notation 1**. : \(\mathbb{N}^{+}\), \(\mathbb{R}\) _and \(\mathbb{R}^{n}\) are defined as the set of positive integers, the set of real numbers and the n-dimensional Euclidean space, respectively. By \(A\leq B\), we mean that \(A-B\) is a seminegative definite matrix.