随机分布参数切换系统的输入输出有限时间稳定与镇定
作者:
中图分类号:

TP273

基金项目:

国家自然科学基金(61863004,62073144)


Input-output finite-time stability and stabilization of stochastic distributed parameter switched systems
Author:
  • 摘要
  • | |
  • 访问统计
  • |
  • 参考文献
  • |
  • 相似文献
  • |
  • 引证文献
  • | |
  • 文章评论
    摘要:

    本文研究了一类随机分布参数切换系统的输入输出有限时间稳定问题.首先,给出了系统在均方意义下输入输出有限时间稳定的概念.其次,通过利用分片Lyapunov-Krasovskii函数、平均驻留时间及线性矩阵不等式等工具,建立了随机分布参数切换系统输入输出有限时间稳定的充分条件;设计一个状态反馈控制器确保相应的闭环系统输入输出有限时间稳定,并以严格的数学推导加以证明.最后,通过两个仿真例子验证了所得结果的有效性.

    Abstract:

    Here the input-output finite-time stability for a class of stochastic distributed parameter switched systems is studied.First, the concept of the input-output finite-time stability of system in mean square sense is given.Second, by using the piecewise Lyapunov-Krasovskii function, average dwell time, linear matrix inequality and other tools, the sufficient conditions of input-output finite-time stability are constructed.In addition, a state feedback controller is designed to ensure the input-output finite-time stability of corresponding closed-loop system, which is proved by strict mathematical derivation.Finally, two simulation examples are given to verify the effectiveness of the results obtained.

    参考文献
    [1] Li Z,Li S Y.Mean square stability of impulsive stochastic delayed reaction-diffusion equations via comparison principle with razumikhin method[J].Journal of Systems Science and Complexity,2020,33(4):1012-1022
    [2] Yao Q,Lin P,Wang L S,et al.Practical exponential stability of impulsive stochastic reaction-diffusion systems with delays[J].IEEE Transactions on Cybernetics,2020.DOI:10.1109/TCYB.2020.3022024
    [3] Dorato P.Short-time stability in linear time-varying systems[D].New York:Polytechnic Institute of Brooklyn,1961
    [4] Li J,Mu X W,Li K.Event-triggered finite-time bounded and finite-time stability for networked control systems under DoS attacks[J].International Journal of Systems Science,2020,51(15):2820-2836
    [5] Gao X B,Ren H R,Deng F Q,et al.Observer-based finite-time H control for uncertain discrete-time nonhomogeneous Markov jump systems[J].Journal of the Franklin Institute,2019,356(4):1730-1749
    [6] Zhang T L,Deng F Q,Zhang W H.Finite-time stability and stabilization of linear discrete time-varying stochastic systems[J].Journal of the Franklin Institute,2019,356(3):1247-1267
    [7] Amato F,Ambrosino R,Cosentino C,et al.Input-output finite time stabilization of linear systems[J].Automatica,2010,46(9):1558-1562
    [8] Guo Y,Yao Y,Wang S C,et al.Input-output finite-time stabilization of linear systems with finite-time boundedness[J].ISA Transactions,2014,53(4):977-982
    [9] 韩晓霞,吴保卫,刘丽丽,等.不确定时变奇异系统的鲁棒输入输出有限时间稳定[J].纺织高校基础科学学报,2015,28(1):72-78 HAN Xiaoxia,WU Baowei,LIU Lili,et al.Robust input-output finite-time stability of time-varying singular systems with uncertainties[J].Basic Sciences Journal of Textile Universities,2015,28(1):72-78
    [10] Liang J X,Wu B W,Wang Y E,et al.Input-output finite-time stability of fractional-order positive switched systems[J].Circuits,Systems,and Signal Processing,2019,38(4):1619-1638
    [11] 杨洋,吴保卫,王月娥.基于事件触发异步切换系统的输入输出有限时间稳定[J].山东大学学报(理学版),2020,55(2):118-126 YANG Yang,WU Baowei,WANG Yue'e.Input-output finite time stability of asynchronous switched systems with event-triggered[J].Journal of Shandong University (Natural Science),2020,55(2):118-126
    [12] Amato F,De Tommasi G,Pironti A.Input-output finite-time stabilization of impulsive linear systems:necessary and sufficient conditions[J].Nonlinear Analysis:Hybrid Systems,2016,19:93-106
    [13] 郭柏灵,蒲学科.随机无穷维动力系统[M].北京:北京航空航天大学出版社,2009
    [14] Krylov N V,Rozovskii B L.Stochastic evolution equations[J].Journal of Soviet Mathematics,1981,16(4):1233-1277
    [15] Kang H W,Zheng L K,Othmer H G.A new method for choosing the computational cell in stochastic reaction-diffusion systems[J].Journal of Mathematical Biology,2012,65(6/7):1017-1099
    [16] Ali M S,Saravanan S,Palanisamy L.Stochastic finite-time stability of reaction-diffusion Cohen-Grossberg neural networks with time-varying delays[J].Chinese Journal of Physics,2019,57:314-328
    [17] Liu X Z,Wu K N,Zhang W H.Mean square finite-time boundary stabilisation and H boundary control for stochastic reaction-diffusion systems[J].International Journal of Systems Science,2019,50(7):1388-1398
    [18] Sun Z D.Switched linear systems:control and design[M].London:Springer Verlag,2005
    [19] Guérin F,Lefebvre D,Mboup A B,et al.Hybrid modeling for performance evaluation of multisource renewable energy systems[J].IEEE Transactions on Automation Science and Engineering,2011,8(3):570-580
    [20] Pellanda P C,Apkarian P,Tuan H D.Missile autopilot design via a multi-channel LFT/LPV control method[J].International Journal of Robust and Nonlinear Control,2002,12(1):1-20
    [21] Li X,Zhou M,Fang X.Finite-time H control of distributed parameter switched systems with event-triggered scheme[J].Asian Journal of Control,2020,2:1-11
    [22] Dai X S,Deng F Q,Luo W G.Stability of stochastic distributed parameter switched systems[C]//Proceedings of the 31st Chinese Control Conference.July 25-27,2012,Hefei,China.IEEE,2012:1585-1589
    [23] Han X X,Wu K N,Ding X H.Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control[J].Applied Mathematics and Computation,2020,385:125422
    [24] Liu K.Stability of infinite dimensional stochastic differential equations with applications[M].New York:Chapman and Hall/CRC,2005
    [25] Zhao P,Feng W,Kang Y.Stochastic input-to-state stability of switched stochastic nonlinear systems[J].Automatica,2012,48(10):2569-2576
    [26] Zhang C L,Deng F Q,Dai X S,et al.Synchronization of reaction-diffusion stochastic complex networks[J].International Journal of Applied and Computational Mathematics,2019,5(1):1-15
    [27] Amato F,Carannante G,De Tommasi G,et al.Input-output finite-time stability of linear systems:necessary and sufficient conditions[J].IEEE Transactions on Automatic Control,2012,57(12):3051-3063
    [28] Blasio G,Kunisch K,Sinestrari E.Stability for abstract linear functional differential equations[J].Israel Journal of Mathematics,1985,50(3):231-263
    [29] Dragomir S S.Some Gronwall type inequalities and applications[M].New York:Nova Science,2003
    相似文献
    引证文献
引用本文

左凰,戴喜生,邓飞其.随机分布参数切换系统的输入输出有限时间稳定与镇定[J].南京信息工程大学学报(自然科学版),2021,13(5):540-547
ZUO Huang, DAI Xisheng, DENG Feiqi. Input-output finite-time stability and stabilization of stochastic distributed parameter switched systems[J]. Journal of Nanjing University of Information Science & Technology, 2021,13(5):540-547

复制
分享
文章指标
  • 点击次数:64
  • 下载次数: 1450
  • HTML阅读次数: 0
  • 引用次数: 0
历史
  • 收稿日期:2021-09-13
  • 在线发布日期: 2021-12-02

地址:江苏省南京市宁六路219号    邮编:210044

联系电话:025-58731025    E-mail:nxdxb@nuist.edu.cn

南京信息工程大学学报 ® 2025 版权所有  技术支持:北京勤云科技发展有限公司