Lyapunov functions in stability of nonlinear systems on time scales

被引：16
|
作者：
Bartosiewicz, Zbigniew [1 ]
Piotrowska, Ewa [1 ]
机构：
[1] Bialystok Tech Univ, Dept Comp Sci, PL-15351 Bialystok, Poland
来源：
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2011年 / 17卷 / 03期
关键词：
asymptotic stability; Lyapunov function; time scale;
D O I：
10.1080/10236190902932734
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Uniform stability and uniform asymptotic stability of nonlinear finite-dimensional systems on arbitrary time scales are studied. Sufficient as well as necessary conditions of stability are given with the aid of Lyapunov functions. They extend known stability criteria for continuous-time and discrete-time systems. The Massera lemma, needed to construct a Lyapunov function for uniformly asymptotically stable systems, is extended to time scales. The role played by the graininess function associated to the time scale is discussed. Some peculiarities that appear for time scales with an unbounded graininess function are exhibited.
引用
收藏
页码：309 / 325
页数：17
相关论文
共 50 条
  • [1] Lyapunov inequalities for a class of nonlinear dynamic systems on time scales
    Taixiang Sun
    Hongjian Xi
    Jing Liu
    Qiuli He
    [J]. Journal of Inequalities and Applications, 2016
  • [2] Lyapunov inequalities for a class of nonlinear dynamic systems on time scales
    Sun, Taixiang
    Xi, Hongjian
    Liu, Jing
    He, Qiuli
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, : 1 - 13
  • [3] Non-monotonic Lyapunov Functions for Stability of Discrete Time Nonlinear and Switched Systems
    Ahmadi, Amir Ali
    Parrilo, Pablo A.
    [J]. 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, : 614 - 621
  • [4] Stochastic Time Scales: Quadratic Lyapunov Functions and Probabilistic Regions of Stability
    Poulsen, Dylan R.
    Davis, John M.
    Gravagne, Ian A.
    [J]. 45TH SOUTHEASTERN SYMPOSIUM ON SYSTEM THEORY, 2013, : 98 - 103
  • [5] LYAPUNOV FUNCTIONS FOR NONLINEAR TIME-VARYING SYSTEMS
    NARENDRA, KS
    TAYLOR, JH
    [J]. INFORMATION AND CONTROL, 1968, 12 (5-6): : 378 - &
  • [6] On the stability and control of nonlinear systems via vector Lyapunov functions
    Nersesov, SG
    Haddad, WM
    [J]. 2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, : 4107 - 4112
  • [7] Indefinite Lyapunov functions based stability of switched nonlinear systems
    Zhang Junfeng
    Zhang Suhuan
    Liu Laiyou
    Cai Xiushan
    [J]. PROCEEDINGS OF THE 32ND 2020 CHINESE CONTROL AND DECISION CONFERENCE (CCDC 2020), 2020, : 5392 - 5397
  • [8] Filtered Lyapunov functions and their applications in the stability analysis of nonlinear systems
    Battilotti, Stefano
    [J]. PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 349 - 354
  • [9] LYAPUNOV FUNCTIONS FOR INVESTIGATING THE GLOBAL STABILITY OF NONLINEAR-SYSTEMS
    AMINOV, AB
    SIRAZETDINOV, TK
    [J]. PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 1985, 49 (06): : 675 - 682
  • [10] On the stability analysis of nonlinear systems using polynomial Lyapunov functions
    Bouzaouache, Hajer
    Braiek, Naceur Benhadj
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2008, 76 (5-6) : 316 - 329
12345