Lyapunov Stability Analysis for Incommensurate Nabla Fractional Order Systems  

作　　者：WEI Yiheng ZHAO Xuan WEI Yingdong CHEN Yangquan 

机构地区：[1]School of Mathematics,Southeast University,Nanjing 211189,China [2]Department of Automation,University of Science and Technology of China,Hefei 230026,China [3]School of Engineering,University of California,Merced,USA

出　　处：《Journal of Systems Science & Complexity》2023年第2期555-576,共22页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.62273092;the Science Climbing Project under Grant No.4307012166;the Anhui Provincial Natural Science Foundation under Grant No.1708085QF141;the Fundamental Research Funds for the Central Universities under Grant No.WK2100100028;the General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2016M602032;the fund of China Scholarship Council under Grant No.201806345002。

摘　　要：This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With the convex assumption,several elementary fractional difference inequalities on Lyapunov functions are developed.According to the essential features of nabla fractional calculus,the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method.To substantiate the efficacy and effectiveness of the theoretical results,four examples are elaborated.

关 键 词：Asymptotic stability ATTRACTIVENESS convex functions difference inequality incommensurate nabla fractional order systems Lyapunov method 

分 类 号：O175[理学—数学]