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连续综合控制系统的状态反馈广义H2 控制

孙凤琪

孙凤琪. 连续综合控制系统的状态反馈广义H2 控制 [J]. 应用数学和力学,2022,43(8):1-10 doi: 10.21656/1000-0887.420169
引用本文: 孙凤琪. 连续综合控制系统的状态反馈广义H2 控制 [J]. 应用数学和力学,2022,43(8):1-10 doi: 10.21656/1000-0887.420169
SUN Fengqi. State Feedback Generalized H2 Control for Continuous Integrated Control System[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420169
Citation: SUN Fengqi. State Feedback Generalized H2 Control for Continuous Integrated Control System[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420169

连续综合控制系统的状态反馈广义H2 控制

doi: 10.21656/1000-0887.420169
基金项目: 国家自然科学基金(61741318)
详细信息
    作者简介:

    孙凤琪(1968—),女,教授,博士(E-mail:1092748497@qq.com

  • 中图分类号: O231.2

State Feedback Generalized H2 Control for Continuous Integrated Control System

  • 摘要: 基于Lyapunov稳定性理论、矩阵分析法、线性矩阵不等式等方法,对同时带有控制输入和干扰输入的奇异摄动时变时滞不确定控制系统进行广义H2控制研究。 设计一个记忆状态广义H2控制器,给出具体设计方法的判定定理。 并对时滞依赖和时滞独立两种情形下采用新的引理,推出保守性相对更小的稳定性判据。 对所得结论进行线性化处理,用数值样例去验证该文所得结论的有效性和可行性。 指出在零到奇异摄动上界的整个区间范围内,闭环系统渐近稳定,扩大了广义H2稳定空间,缩小了L2-L的性能指标。通过与相关文献进行稳定态指标对比,展示出该文所得方法具有一定的优越性和较小的保守性,并且适用于标准和非标准情形。
  • 表  1  广义H2稳定性能指标对比

    Table  1.   Comparison of generalized H2 stability performance indicators

    methodgeneralized H2 control gain matrix ${\boldsymbol{K}}$optimal ${L_2} {\text{-}} {L_\infty }$ performance index ${\gamma ^ * }$perturbation upper bound $\bar \varepsilon $
    ref. [12]${{\boldsymbol{K}}_1} = [ {\begin{array}{*{20}{c}} { - 22.046\;7}&{ - 14.167\;5} \end{array}} ]$1.32550.3
    ${{\boldsymbol{K}}_2} = [ {\begin{array}{*{20}{c}} { - 22.037\;6}&{ - 12.656\;2} \end{array}} ]$
    theorem 2$K = [ {\begin{array}{*{20}{c}} { - 2.252\;4}&{0.023\;6} \end{array}} ]$1.1265 0.35
    ${K_1} = [ {\begin{array}{*{20}{c}} {0.305\;7}&{0.044\;3} \end{array}} ]$
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-06-22
  • 录用日期:  2021-09-06
  • 修回日期:  2021-09-06
  • 网络出版日期:  2022-06-20

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