基于Razumikhin-Type理论的中立性随机切换非线性系统的P阶矩稳定性与几乎必然稳定性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 970-983.

基于Razumikhin-Type理论的中立性随机切换非线性系统的P阶矩稳定性与几乎必然稳定性

谷海波^1,*(),高彩霞²()

¹ 中国科学院数学与系统科学研究院北京 100190
² 内蒙古大学数学科学学院呼和浩特 010021

收稿日期:2017-03-14 出版日期:2018-11-09 发布日期:2018-11-09
通讯作者: 谷海波 E-mail:guhaibo@amss.ac.cn;gaocx0471@163.com
作者简介:高彩霞, E-mail:gaocx0471@163.com
基金资助:
国家自然科学基金(11261033)

Razumikhin-Type Theorems on P-th Moment and Almost Sure Stability of Neutral Stochastic Switched Nonlinear Systems

Haibo Gu^1,*(),Caixia Gao²()

¹ Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
² School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021

Received:2017-03-14 Online:2018-11-09 Published:2018-11-09
Contact: Haibo Gu E-mail:guhaibo@amss.ac.cn;gaocx0471@163.com
Supported by:
the NSFC(11261033)

摘要/Abstract

摘要：

研究了中立型随机切换非线性系统的P阶矩稳定性与几乎必然稳定性.采用Lyapunov-Razumikhin方法和随机分析技术，建立了中立型随机切换非线性系统稳定性的判别准则，给出了中立型随机切换非线性系统稳定的充分条件.最后通过仿真算例表明了所得结果的有效性.

关键词: 中立型随机切换非线性系统, P阶矩稳定性, 几乎必然稳定性, Lyapunov-Razumikhin方法

Abstract:

In this paper, P-th moment and almost sure stability for a class of neutral stochastic switched nonlinear systems have been investigated. By utilizing Lyapunov-Razumikhin approach, we employ the stochastic analysis techniques to establish novel stability criteria for neutral stochastic switched nonlinear systems. Some sufficient conditions have been derived to check the stability of the neutral stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effectiveness of the results.

Key words: Neutral stochastic switched nonlinear system, P-th moment stability, Almost surely stability, Lyapunov-Razumikhin approach

中图分类号:

O231.2

谷海波,高彩霞. 基于Razumikhin-Type理论的中立性随机切换非线性系统的P阶矩稳定性与几乎必然稳定性[J]. 数学物理学报, 2018, 38(5): 970-983.

Haibo Gu,Caixia Gao. Razumikhin-Type Theorems on P-th Moment and Almost Sure Stability of Neutral Stochastic Switched Nonlinear Systems[J]. Acta mathematica scientia,Series A, 2018, 38(5): 970-983.

图/表 2

参考文献 20

1	Hale J , Lunel S . Introduction to Functional Differential Equations. Berlin: Springer-Verlag, 1993
2	Chatterjee D , Liberzon D . On stability of switched stochastic systems. IEEE Conference on Decision and Control, 2004, 4 (4): 4125- 4127
3	Feng W , Tian J , Zhao P . Stability analysis of switched stochastic systems. Automatica, 2011, 47 (1): 148- 157 doi: 10.1016/j.automatica.2010.10.023
4	Chen G , Xiang Z , Mahmoud M . Stability and H_∞ performance analysis of switched stochastic neutral systems. Circ Syst Signal Pr, 2013, 32 (1): 387- 400 doi: 10.1007/s00034-012-9459-1
5	Kolmanovskii V , Nosov V . Stability of Functional Differential Equations. New York: Academic Press, 1986
6	Chen H , Shi P , Lim C , et al. Exponential stability for neutral stochastic markov systems with time varying delay and its applications. IEEE Trans on Cybern, 2016, 46 (6): 1350- 1362 doi: 10.1109/TCYB.2015.2442274
7	Razumikhin B . On the stability of systems with delay. Prikl Mat Mekh, 1956, 20: 500- 512
8	Razumikhin B . Application of Lyapunov's method to problems in the stability of systems with a delay. Automation and Remote Control, 1960, 21 (6): 740- 749
9	Mao X . Stochastic Differential Equations and Applications. Chichester: Horwood Publications, 1997
10	Mao X . Razumikhin-type theorems on exponential stability of stochastic functional differential equations. Stoch Proc Appl, 1996, 65 (2): 233- 250 doi: 10.1016/S0304-4149(96)00109-3
11	Mao X . Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations. SIAM J Math Anal, 1997, 28 (2): 389- 401 doi: 10.1137/S0036141095290835
12	Yang Z , Zhu E , Xu Y , et al. Razumikhin-type theorems on exponential stability of stochastic functional differential equations with infinite delay. Acta Appl Math, 2010, 111B (2): 219- 231
13	Pavlovic G , Jankovic S . Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay. J Comput Appl Math, 2012, 236 (7): 1679- 1690 doi: 10.1016/j.cam.2011.09.045
14	Wu F , Hu S , Mao X . Razumikhin-type theorem for neutral stochastic functional differential equations with unbounded delay. Acta Mathematica Sinica, 2011, 31B (4): 1245- 1258
15	Cheng P , Deng F . Global exponential stability of impulsive stochastic functional differential systems. Statis and Prob Lett, 2010, 80 (23/24): 1854- 1862
16	Wu X , Zhang W , Tang Y . P-th moment stability of impulsive stochastic delay differential systems with markovian switching. Commun Nonlinear Sci Numer Simul, 2013, 18 (7): 1870- 1879 doi: 10.1016/j.cnsns.2012.12.001
17	Peng S , Jia B . Some criteria on p-th moment stability of impulsive stochastic functional differential equations. Statis Prob Lett, 2010, 80 (13): 1085- 1092
18	Hu S , Huang C , Wu F . Stochastic Differential Equations. Beijing: Science Press, 2008
19	Wu F , Hu S . Razumikhin-type theorems on general decay stability and robustness for stochastic functional differential equations. Int J Robust Nonlinear Control, 2012, 22 (22): 763- 777
20	Chatterjee D , Liberzon D . Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions. SIAM J Control Opti, 2006, 45 (1): 174- 206 doi: 10.1137/040619429