| On stability of discontinuous systems via vector Lyapunov functions |
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| 作者姓名： | 慕小武 程桂芳 丁志帅 |
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| 作者单位： | Department of Mathematics Zhengzhou University，Department of Mathematics，Zhengzhou University，Department of Mathematics，Zhengzhou University，Zhengzhou 450052，P.R.China，Zhengzhou 450052，P.R.China，Zhengzhou 450052，P.R.China |
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| 摘 要： | This paper deals with the stability of systems with discontinuous right- hand 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 discontinu- ous systems based on locally Lipschitz continuous and regular vector Lyapunov functions.
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| 关 键 词： | Filippov解 对照原则 稳定性 Lyapunov函数 不连续系统 |
| 收稿时间： | 2006-07-04 |
On stability of discontinuous systems via vector Lyapunov functions |
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| Mu Xiao-wu,Cheng Gui-fang,Ding Zhi-shuai.On stability of discontinuous systems via vector Lyapunov functions[J].Applied Mathematics and Mechanics(English Edition),2007,28(12):1613-1619. |
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| Authors: | Mu Xiao-wu Cheng Gui-fang Ding Zhi-shuai |
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| Institution: | Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China |
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| Abstract: | This paper deals with the stability of systems with discontinuous right- hand 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 discontinu- ous systems based on locally Lipschitz continuous and regular vector Lyapunov functions. |
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| Keywords: | Filippov solutions comparison principles stability vector Lyapunov functions discontinuous systems |
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