离散时间两层切换系统的鲁棒指数几乎处处稳定性

宋杨; 杨杰; 郑敏; 费敏锐

doi:10.16383/j.aas.2016.c150441

离散时间两层切换系统的鲁棒指数几乎处处稳定性

doi: 10.16383/j.aas.2016.c150441 cstr: 32138.14.j.aas.2016.c150441

宋杨^1,2, ,,
杨杰^1,,
郑敏^1,2,,
费敏锐^1,2,

1.
上海大学机电工程与自动化学院上海 200072
2.
上海市电站自动化技术重点实验室上海 200072

基金项目:

上海市科委项目 14JC1402200

国家重大科学仪器设备开发专项课题 2012YQ15008703

国家自然科学基金 61573237

上海市自然科学基金 13ZR1416300

详细信息

作者简介:
杨杰上海大学机电工程与自动化学院硕士研究生.主要研究方向为切换系统.E-mail:yangjielanz@163.com

郑敏上海大学机电工程与自动化学院副研究员.主要研究方向为网络控制系统,时滞系统和神经网络.E-mail:zhengmin203@163.com

费敏锐上海大学机电工程与自动化学院教授.主要研究方向为网络化控制系统及实现.E-mail:mrfei@staff.shu.edu.cn

通讯作者:
宋杨上海大学机电工程与自动化学院副研究员.主要研究方向为切换系统,网络控制理论与应用.本文的通信作者.E-mail:y_song@shu.edu.cn

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- 被引次数: 0
出版历程
- 收稿日期: 2015-07-08
- 录用日期: 2015-09-23
- 刊出日期: 2016-01-01

Robust Exponential Almost Sure Stability of Discrete-time Two-level Switched Systems

SONG Yang^{1,2
, ,},
YANG Jie^1
,,
ZHENG Min^{1,2
,},
FEI Min-Rui^{1,2
,}

1.
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072
2.
Shanghai Key Laboratory of Power Station Automation Technology, Shanghai 200072

Funds:

Science and Technology Commission of Shanghai Municipality 14JC1402200

National Key Scientific Instrument and Equipment Development Project 2012YQ15008703

National Natural Science Foundation of China 61573237

Natural Science Foundation of Shanghai 13ZR1416300

More Information

Author Bio:
Master student at the School of Mechatronics Engineering and Automation, Shanghai University. His main research interest is switched systems

Associate professor at the School of Mechatronic Engineering and Automation, Shanghai University. His research interest covers networked control systems, time delay systems and neural networks

Professor at the School of Mechatronics Engineering and Automation, Shanghai University. His research interest covers networked control system and its implementation

Corresponding author: SONG Yang Associate professor at the School of Mechatronic Engineering and Automation, Shanghai University. His research interest covers switched systems, networked control theory and application. Corresponding author of this paper

摘要

摘要: 提出了一种新类型的切换系统——两层切换系统(Two-level switched systems, TSSs),其顶层切换是确定的,底层切换为随机的且由多个Markov链支配.基于持续驻留时间(Persistent dwell-time, PDT)方法,研究了TSS存在参数不确定性情况下的鲁棒指数几乎处处(Exponential almost sure, EAS)稳定性,以线性矩阵不等式(Linear matrix inequality, LMI)形式给出了一个充分条件.最后通过数值仿真例子验证了本文方法的有效性.
- 两层切换系统 /
- 持续驻留时间 /
- 鲁棒指数几乎处处稳定 /
- 离散随机系统
Abstract: This paper proposes a new type of switched systems called two-level switched systems(TSSs). In a TSS, the top-level switching is deterministic, while the low-level switching is governed by multiple Markov chains and thus it is stochastic. Considering a TSS with parameter uncertainties, the robust exponential almost sure(EAS) stability is investigated. Based on the method of persistent dwell-time(PDT), a sufficient condition of robust EAS stability is given in the form of linear matrix inequalities(LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed result.
- Two-level switched systems /
- persistent dwell-time /
- robust exponential almost sure stability /
- discrete-time stochastic system

HTML全文

图 1 SD-MJLS/S-MJLS示意图

Fig. 1 Schematic diagram of SD-MJLS/S-MJLS

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图 2 两层切换系统

Fig. 2 Two-level switched systems

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图 3 PDT切换示意图

Fig. 3 Schematic diagram of PDT switching

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图 4 PDT第 $p$ 阶段的切换序列

Fig. 4 The $p$ - $th$ stage switching sequence of PDT

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图 5 $\gamma (k)$ 的切换序列

Fig. 5 Switching sequence of $\gamma (k)$

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图 6 $\ln || {{{\mathit{\boldsymbol{x}}}_k}} ||$ 的7次样本实现

Fig. 6 Seven realizations of $\ln || {{{\mathit{\boldsymbol{x}}

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参考文献(18)

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[2]	Zhao X D, Zhang L X, Shi P, Liu M. Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Transactions on Automatic Control, 2012, 57(2):1809-1815 http://ieeexplore.ieee.org/document/6097035/
[3]	Hespanha J P. Uniform stability of switched linear systems:extensions of LaSalle's invariance principle. IEEE Transactions on Automatic Control, 2004, 49(4):470-482 doi: 10.1109/TAC.2004.825641
[4]	Zhang L X, Zhuang S L, Shi P. Non-weighted quasi-time-dependent H_∞ filtering for switched linear systems with persistent dwell-time. Automatica, 2015, 54:201-209 doi: 10.1016/j.automatica.2015.02.010
[5]	Zhu J, Wang L P, Spiryagin M. Control and decision strategy for a class of Markovian jump systems in failure prone manufacturing process. IET Control Theory & Applications, 2012, 6(12):1803-1811
[6]	Mao Z, Jiang B, Shi P. H_∞ fault detection filter design for networked control systems modelled by discrete Markovian jump systems. IET Control Theory & Applications, 2007, 1(5):1336-1343 http://ieeexplore.ieee.org/document/4293139/keywords
[7]	马卫国, 邵诚. 网络控制系统随机稳定性研究. 自动化学报, 2007, 33(8):878-882 http://www.aas.net.cn/CN/abstract/abstract17261.shtml Ma Wei-Guo, Shao Cheng. Stochastic stability for networked control systems. Acta Automatica Sinica, 2007, 33(8):878-882 http://www.aas.net.cn/CN/abstract/abstract17261.shtml
[8]	Xiao N, Xie L H, Fu M Y. Stabilization of Markov jump linear systems using quantized state feedback. Automatica 2010, 46(10):1696-1702 doi: 10.1016/j.automatica.2010.06.018
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[10]	Fang Y G, Loparo K A. Stabilization of continuous-time jump linear systems. IEEE Transactions on Automatic Control, 2002, 47(10):1590-1603 doi: 10.1109/TAC.2002.803528
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[13]	Bolzern P, Colaneri P, De Nicolao G. Almost sure stability of Markov jump linear systems with deterministic switching. IEEE Transactions on Automatic Control, 2013, 58(1):209-214 doi: 10.1109/TAC.2012.2203049
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离散时间两层切换系统的鲁棒指数几乎处处稳定性

doi: 10.16383/j.aas.2016.c150441 cstr: 32138.14.j.aas.2016.c150441

通讯作者:
宋杨上海大学机电工程与自动化学院副研究员.主要研究方向为切换系统,网络控制理论与应用.本文的通信作者.E-mail:y_song@shu.edu.cn

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Robust Exponential Almost Sure Stability of Discrete-time Two-level Switched Systems

Corresponding author: SONG Yang Associate professor at the School of Mechatronic Engineering and Automation, Shanghai University. His research interest covers switched systems, networked control theory and application. Corresponding author of this paper

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离散时间两层切换系统的鲁棒指数几乎处处稳定性

doi: 10.16383/j.aas.2016.c150441 cstr: 32138.14.j.aas.2016.c150441

通讯作者: 宋杨 上海大学机电工程与自动化学院副研究员.主要研究方向为切换系统,网络控制理论与应用.本文的通信作者.E-mail:y_song@shu.edu.cn

计量

出版历程

Robust Exponential Almost Sure Stability of Discrete-time Two-level Switched Systems

Corresponding author: SONG Yang Associate professor at the School of Mechatronic Engineering and Automation, Shanghai University. His research interest covers switched systems, networked control theory and application. Corresponding author of this paper

计量

出版历程

目录

通讯作者:
宋杨上海大学机电工程与自动化学院副研究员.主要研究方向为切换系统,网络控制理论与应用.本文的通信作者.E-mail:y_song@shu.edu.cn