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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

宋杨 杨杰 郑敏 费敏锐

宋杨, 杨杰, 郑敏, 费敏锐. 离散时间两层切换系统的鲁棒指数几乎处处稳定性. 自动化学报, 2016, 42(1): 131-139. doi: 10.16383/j.aas.2016.c150441
引用本文: 宋杨, 杨杰, 郑敏, 费敏锐. 离散时间两层切换系统的鲁棒指数几乎处处稳定性. 自动化学报, 2016, 42(1): 131-139. doi: 10.16383/j.aas.2016.c150441
SONG Yang, YANG Jie, ZHENG Min, FEI Min-Rui. Robust Exponential Almost Sure Stability of Discrete-time Two-level Switched Systems. ACTA AUTOMATICA SINICA, 2016, 42(1): 131-139. doi: 10.16383/j.aas.2016.c150441
Citation: SONG Yang, YANG Jie, ZHENG Min, FEI Min-Rui. Robust Exponential Almost Sure Stability of Discrete-time Two-level Switched Systems. ACTA AUTOMATICA SINICA, 2016, 42(1): 131-139. 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
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

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

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: 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.
  • 图  1  SD-MJLS/S-MJLS示意图

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

    图  2  两层切换系统

    Fig.  2  Two-level switched systems

    图  3  PDT切换示意图

    Fig.  3  Schematic diagram of PDT switching

    图  4  PDT第 $p$ 阶段的切换序列

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

    图  5  $\gamma (k)$ 的切换序列

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

    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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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

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