Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach  

作　　者：Shenquan Wang Wenchengyu Ji Yulian Jiang Yanzheng Zhu Jian Sun 

机构地区：[1]College of Electrical and Electronic Engineering,Changchun University of Technology,Changchun 130012,China [2]the College of Electrical Engineering and Automation,Shandong University of Science and Technology,Qingdao 266590,China [3]Key Laboratory of Complex Systems Intelligent Control and Decision,Beijing Institute of Technology,Beijing 100081,China

出　　处：《IEEE/CAA Journal of Automatica Sinica》2024年第4期996-1006,共11页自动化学报（英文版）

基　　金：the National Natural Science Foundation of China(62273058,U22A2045);the Key Science and Technology Projects of Jilin Province(20200401075GX);the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province(20230508043RC)。

摘　　要：This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

关 键 词：Equivalent reciprocal combination technique quadratic function convex approximation approach STABILITY timevarying delay 

分 类 号：O175[理学—数学]