| 基于向量Liapunov函数不连续系统的稳定性研究 |
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| 引用本文： | 慕小武,程桂芳,丁志帅.基于向量Liapunov函数不连续系统的稳定性研究[J].应用数学和力学,2007,28(12):1441-1447. |
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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： | 郑州大学 数学系,郑州 450052 |
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| 摘 要： | 基于局部Lipschitz连续且正则(Clarke意义下)的向量Liapunov函数，讨论不连续自治系统的稳定性(Filippov解意义下)．通过定义一类新的向量Liapunov函数的“集值导数”，给出了关于不连续系统的广义比较原理．基于Lipschitz连续且正则的向量Liapunov函数，进一步的给出不连续自治系统的Liapunov稳定性定理．
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| 关 键 词： | Filippov解 比较原理 稳定性 向量Liapunov函数 不连续系统 |
| 文章编号： | 1000-0887（2007）12-1441-07 |
| 收稿时间： | 2006-07-04 |
| 修稿时间： | 2006-07-04 |
On the Stability of Discontinuous Systems via Vector Liapunov Functions |
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| MU Xiao-wu,CHENG Gui-fang,DING Zhi-shuai.On the Stability of Discontinuous Systems via Vector Liapunov Functions[J].Applied Mathematics and Mechanics,2007,28(12):1441-1447. |
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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: | The stability of systems with discontinuous right-hand side(with solutions in Filippov's sense) via locally Lipschitz continuous and regular vector Liapunov functions are discussed.A new type of "set-valued derivative" of vector Liapunov functions was introduced,some generalized comparison principles on discontinuous systems were shown.Furthermore Liapunov stability theory was developed for a class of discontinuous systems based on locally Lipschitz continuous and regular vector Liapunov functions. |
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| Keywords: | Filippov solutions comparison principles stability vector Liapunov functions discontinuous systems |
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