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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (8): 1069-1075.doi: https://doi.org/10.1007/s10483-009-0814-y

• Articles • 上一篇    

Finite-time stability with respect to a closed invariant set for a class of discontinuous systems

程桂芳1,2 慕小武1   

  1. 1. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, P. R. China;
    2. Physical Engineering College, Zhengzhou University, Zhengzhou 450001, P. R. China
  • 收稿日期:2008-10-31 修回日期:2009-06-22 出版日期:2009-08-01 发布日期:2009-08-01

Finite-time stability with respect to a closed invariant set for a class of discontinuous systems

 CHENG Gui-Fang1,2, MU Xiao-Wu1   

  1. 1. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, P. R. China;
    2. Physical Engineering College, Zhengzhou University, Zhengzhou 450001, P. R. China
  • Received:2008-10-31 Revised:2009-06-22 Online:2009-08-01 Published:2009-08-01

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摘要： This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.

关键词: Filippov solution, closed invariant set, finite-time stability, discontinuous system

Abstract: This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.

Key words: Filippov solution, closed invariant set, finite-time stability, discontinuous system

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