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On stability of discontinuous systems via vector Lyapunov functions 被引量：2

On stability of discontinuous systems via vector Lyapunov functions
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摘要 This paper deals with the stability of systems with discontinuous righthand side （with solutions in Filippov＇s sense） via locally Lipschitz continuous and regular vector Lyapunov functions. A new type of “set-valued derivative” of vector Lyapunov functions is introduced, some generalized comparison principles on discontinuous systems are shown. Furthermore, Lyapunov stability theory is developed for a class of discontinuous systems based on locally Lipschitz continuous and regular vector Lyapunov functions. This paper deals with the stability of systems with discontinuous righthand side （with solutions in Filippov＇s sense） via locally Lipschitz continuous and regular vector Lyapunov functions. A new type of “set-valued derivative” of vector Lyapunov functions is introduced, some generalized comparison principles on discontinuous systems are shown. Furthermore, Lyapunov stability theory is developed for a class of discontinuous systems based on locally Lipschitz continuous and regular vector Lyapunov functions.
作者 慕小武 程桂芳 丁志帅
机构地区 Department of Mathematics
出处 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第12期1613-1619,共7页 应用数学和力学（英文版）
关键词 Filippov solutions comparison principles STABILITY vector Lyapunov functions discontinuous systems Filippov solutions, comparison principles, stability, vector Lyapunov functions, discontinuous systems
分类号 O231.2 [理学—运筹学与控制论]
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参考文献11

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同被引文献24

  • 1慕小武,程桂芳,唐风军.非自治非光滑系统的Matrosov稳定性定理[J].应用数学学报,2007,30(1):168-175. 被引量：6
  • 2Filippov A F. Differential Equations with Discontinuous Right-hand Sides[M]. Dordreeht, The Netherlands: Kluwer, 1988.
  • 3Rouche N, Mawhin J. Ordinary Differential Equations Ⅱ: Stability and Periodical Solutions[M]. London, U. K: Pitman, 1980.
  • 4Paden B, Pania R. Globally asymptotically stable PD+ Controller for robot manipulators [J]. International Journal of Control, 1988,47 : 1697-1712.
  • 5Loria A, Panteley E, Popovic D, Teel A R. A nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems [J]. IEEE Transactions on Automatic Control, 2005,50 (2):183- 197.
  • 6Teel A, Panteley E, Loria A. Integral characterizations of uniform asymptotic and exponential stability with applieations[J]. Math Control Signals Syst,2002,15:177-201.
  • 7Mazenc F. Strict lyapunov functions for time-varying systems[J]. Automatica,2003,39: 349-353.
  • 8Mazenc F, Nesic D. Strong lyapunov functions for systems satisfying the conditions of LaSalle[J]. IEEE Transactions on Automatic Control, 2004,49 (6) : 1026-1060.
  • 9Daniel Shevitz, Bard Paden. Lyapunov stability theory of nonsmooth systems [J]. IEEE Transactions on Automatic Control, 1994,39(9) : 1910-1914.
  • 10Orlov Y. Extended invariance principle for nonautonomoos switched systems [J]. IEEE Transactions on Automatic Control, 2003,48 (8) : 1448-1452.

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Applied Mathematics and Mechanics(English Edition)
2007年 第12期

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