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周期离散时间系统的$L_{2}$-$L_{\infty}$预见控制

李丽1,3, 廖永龙2, 孟晓华1,3   

  1. 1. 湖北经济学院 信息管理与统计学院, 武汉 430205;
    2. 北京石 油化工学院 致远学院, 北京 102617;
    3. 湖北经济学院 湖北数据与分析中心, 武汉 430205
  • 收稿日期:2021-04-13 修回日期:2021-09-25 出版日期:2022-05-25 发布日期:2022-07-23
  • 通讯作者: 廖永龙,Email:liaoyonglong@bipt.edu.cn.
  • 基金资助:
    国家自然科学资助课题(61903130),湖北省教育厅科研重点项目(D20192202),湖北经济学院科研培育项目(PYZD202005,PYYB202007),北京市教育委员会科技计划一般项目(KM202110017002)资助课题.

李丽, 廖永龙, 孟晓华. 周期离散时间系统的$L_{2}$-$L_{\infty}$预见控制[J]. 系统科学与数学, 2022, 42(5): 1113-1128.

LI Li, LIAO Yonglong, MENG Xiaohua. L2-L Preview Control for Discrete-Time Periodic Systems[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(5): 1113-1128.

L2-L Preview Control for Discrete-Time Periodic Systems

LI Li1,3, LIAO Yonglong2, MENG Xiaohua1,3   

  1. 1. School of Information Management and Statistics, Hubei University of Economics, Wuhan 430205;
    2. ZHIYUAN College, Beijing Institute of Petrochemical Technology, Beijing 102617;
    3. Hubei Center for Data and Analysis, Hubei University of Economics, Wuhan 430205
  • Received:2021-04-13 Revised:2021-09-25 Online:2022-05-25 Published:2022-07-23
文章研究了一类周期离散时间系统的$L_{2}$-$L_{\infty}$预见控制问题.通过引入辅助变量,用系统状态向量及输入向量与相应辅助变量之差代替通常的状态差分,构造出周期扩大误差系统,将$L_{2}$-$L_{\infty}$预见控制问题转化为扩大误差系统的输出反馈控制问题.针对扩大误差系统,利用Lyapunov第二方法并结合LMI技术,给出了闭环系统渐近稳定及满足$L_{2}$-$L_{\infty}$性能的充分条件.数值仿真表明了文章结果的有效性.
In this paper, the L2-L preview control problem of discrete-time periodic systems is studied. By introducing auxiliary variables and replacing the usual state difference with the difference between the system state vector and the input vector and the corresponding auxiliary variables, a periodic augmented error system is constructed. As a result, the L2-L preview control problem is converted into an output feedback control problem. For the augmented error system, sufficient conditions are derived to assure the asymptotic stability with an L2-L performance by the Lyapunov second method and LMI technology. A numerical simulation example illustrates the effectiveness of the results.

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