| A Notion of Stochastic Input-to-State Stability and Its Application to Stability of Cascaded Stochastic Nonlinear Systems |
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| 作者姓名： | Shu-jun Liu Ji-feng Zhang Zhong-ping Jiang |
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| 作者单位： | [1]Department of Mathematics, Southeast University, Nanjing 210096, China [2]Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China [3]Department of Electrical and Computer Engineering, Polytechnic University, 5 Metrotech Center, Brooklyfl, N.Y. 11201, USA |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No.60221301, No.60428304）. |
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| 摘 要： | In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.
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| 关 键 词： | 随机非线性系统 李雅普诺夫函数 概率论 稳定性 |
| 收稿时间： | 2007-01-08 |
| 修稿时间： | 2007-04-27 |
A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems |
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| Shu-jun Liu Ji-feng Zhang Zhong-ping Jiang.A Notion of Stochastic Input-to-State Stability and Its Application to Stability of Cascaded Stochastic Nonlinear Systems[J].Acta Mathematicae Applicatae Sinica,2008,24(1):141-156. |
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| Authors: | Shu-jun Liu Ji-feng Zhang Zhong-ping Jiang |
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| Institution: | (1) Department of Mathematics, Southeast University, Nanjing, 210096, China;(2) Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China;(3) Department of Electrical and Computer Engineering, Polytechnic University, 5 Metrotech Center, Brooklyn, N.Y. 11201, USA |
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| Abstract: | In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems
are investigated in the stochastic framework. Firstly, the notion of (practical) stochastic input-to-state stability with
respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov
function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.
Supported by the National Natural Science Foundation of China (No.60221301, No.60428304). |
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| Keywords: | Stochastic nonlinear systems Stochastic input-to-state stability (SISS) SISS-Lyapunov function |
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