{"title":"Lyapunov-based stability of time-triggered impulsive logical dynamic networks","authors":"Xueying Ding , Jianquan Lu , Xiangyong Chen","doi":"10.1016/j.nahs.2023.101417","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the stability of impulsive logical dynamic systems (ILDNs) from two aspects: impulsive disturbance and impulsive control. The existing results on the stability of ILDNs only consider the stability of ILDNs under a given impulsive instant sequence (IIS), which has some limitations and motivates us to consider the stability of ILDNs under any IIS. By constructing a merged ILDN, under the assumption that the non-impulsive process and impulsive process are all globally stable, a necessary and sufficient condition on the stability of ILDNs under any IIS is proposed at first. Unfortunately, the obtained result is too restrictive, and in practice, it is not common that a stable LDN is still stable under any IIS. The fact is that for any stable LDN, there exist some IISs such that its stability is destroyed, and these IISs are called impulsive disturbances; for any unstable LDN, there exist some IISs such that the stability can be achieved, and these IISs are called impulsive control. To investigate the stability of ILDNs, the concept of average impulsive interval is first introduced to ILDNs, and several sufficient conditions are proposed to ensure the stability of LDNs under the time-triggered IISs with the property of average impulsive interval. Moreover, the obtained results are applied to the set stability of ILDNs.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Hybrid Systems","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1751570X23000882","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the stability of impulsive logical dynamic systems (ILDNs) from two aspects: impulsive disturbance and impulsive control. The existing results on the stability of ILDNs only consider the stability of ILDNs under a given impulsive instant sequence (IIS), which has some limitations and motivates us to consider the stability of ILDNs under any IIS. By constructing a merged ILDN, under the assumption that the non-impulsive process and impulsive process are all globally stable, a necessary and sufficient condition on the stability of ILDNs under any IIS is proposed at first. Unfortunately, the obtained result is too restrictive, and in practice, it is not common that a stable LDN is still stable under any IIS. The fact is that for any stable LDN, there exist some IISs such that its stability is destroyed, and these IISs are called impulsive disturbances; for any unstable LDN, there exist some IISs such that the stability can be achieved, and these IISs are called impulsive control. To investigate the stability of ILDNs, the concept of average impulsive interval is first introduced to ILDNs, and several sufficient conditions are proposed to ensure the stability of LDNs under the time-triggered IISs with the property of average impulsive interval. Moreover, the obtained results are applied to the set stability of ILDNs.
期刊介绍:
Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.