A smooth converse Lyapunov theorem for robust stability

被引：588
作者：
Lin, YD [1 ]
Sontag, ED [1 ]
Wang, Y [1 ]
机构：
[1] RUTGERS STATE UNIV,DEPT MATH,NEW BRUNSWICK,NJ 08903
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1996年 / 34卷 / 01期
关键词：
nonlinear stability; stability with respect to sets; Lyapunov function techniques; robust stability;
D O I：
10.1137/S0363012993259981
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper presents a converse Lyapunov function theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets.
引用
收藏
页码：124 / 160
页数：37
相关论文
共 33 条
  • [1] [Anonymous], 1992, P NOLCOS 92 BORD FRA
  • [2] Aubin J.-P., 1991, Viability Theory
  • [3] Aubin J. P., 1984, Differential inclusions: Set-valued maps and viability theory
  • [4] Bhatia N. P., 1970, STABILITY THEORY DYN
  • [5] Brocker T., 1975, DIFFERENTIABLE GERMS, DOI 10.1017/cbo9781107325418
  • [6] Federer H., 1969, GEOMETRIC MEASURE TH
  • [7] Hirsch M. W., 1976, GraduateTexts inMathematics, V33
  • [8] KALOUPTSIDIS N, 1982, MATH SYST THEORY, V15, P323
  • [9] KALOUPTSIDIS N, 1977, ACCESSIBILITY STABIL
  • [10] A TOOLKIT FOR NONLINEAR FEEDBACK DESIGN
    KANELLAKOPOULOS, I
    KOKOTOVIC, PV
    MORSE, AS
    [J]. SYSTEMS & CONTROL LETTERS, 1992, 18 (02) : 83 - 92
1234