On the Stability of Linear Time-Varying Differential Equations

被引：2
作者：
Zaitsev, V. A. [1 ]
Kim, I. G. [1 ]
机构：
[1] Udmurt State Univ, Izhevsk 426034, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2022年 / 319卷 / SUPPL 1期
关键词：
linear differential equations; stability; time-varying system; stable polynomial; Kharitonov's theorem; robust stability; SUFFICIENT CONDITIONS;
D O I：
10.1134/S0081543822060268
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The article discusses the stability of linear differential equations with time-varying coefficients.It is shown that, in contrast to equations with time-invariant coefficients, the condition for the characteristicpolynomial to be Hurwitz for a linear differential equation with time-varying coefficients is neither necessarynor sufficient for the asymptotic stability of the differential equation. It is proved that the analog of Kharitonov'stheorem on robust stability does not hold if the coefficients of the differential equation are time-varying.
引用
收藏
页码：S298 / S317
页数：20
相关论文
共 50 条
  • [31] Stability criterion and stabilization of linear time-varying systems
    Tan, Feng
    Duan, Guangren
    PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, : 3238 - 3243
  • [32] Linear Singular Continuous Time-varying Delay Equations: Stability and Filtering via LMI Approach
    Phat, Vu Ngoc
    Thanh, Nguyen Truong
    ACTA MATHEMATICA VIETNAMICA, 2024, 49 (04) : 595 - 609
  • [33] Internally positive representations and stability analysis of linear differential systems with multiple time-varying delays
    De Iuliis, Vittorio
    D'Innocenzo, Alessandro
    Germani, Alfredo
    Manes, Costanzo
    IET CONTROL THEORY AND APPLICATIONS, 2019, 13 (07) : 920 - 927
  • [34] Asymptotic behaviors of solutions of a class of time-varying differential equations
    Hammi, Mekki
    Hammami, Mohamed Ali
    Eddine, Abbes Imad
    GEORGIAN MATHEMATICAL JOURNAL, 2023, 30 (01) : 95 - 109
  • [35] TIME-VARYING COEFFICIENTS NEUTRAL DIFFERENTIAL EQUATIONS: ON ASYMPTOTIC PROPERTIES
    Moulai -Khatir, Anes
    DIFFERENTIAL EQUATIONS & APPLICATIONS, 2022, 14 (04): : 525 - 532
  • [36] STABILITY OF THE HEAT AND OF THE WAVE EQUATIONS WITH BOUNDARY TIME-VARYING DELAYS
    Nicaise, Serge
    Valein, Julie
    Fridman, Emilia
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2009, 2 (03): : 559 - 581
  • [37] Feedback stability of discrete-time, linear time-varying systems
    Orlowski, P.
    2008 MEDITERRANEAN CONFERENCE ON CONTROL AUTOMATION, VOLS 1-4, 2008, : 592 - 597
  • [38] QC CHARACTERIZATIONS FOR THE CLOSED-LOOP STABILITY OF TIME-VARYING LINEAR SYSTEMS
    Liu, Liu
    Lu, Yufeng
    ASIAN JOURNAL OF CONTROL, 2014, 16 (06) : 1744 - 1750
  • [39] -stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations
    Wang, Lei
    Li, Xiaodi
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (11) : 1140 - 1446
  • [40] CHARACTERISTIC MATRICES AND SIMILARITY OF TIME-VARYING LINEAR DIFFERENTIAL SYSTEMS
    邓飞其
    刘永清
    冯昭枢
    Annals of Applied Mathematics, 1997, (01) : 10 - 15
12345