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Volume 28 Issue 1
Jan.  2002
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Journal of Beijing University of Aeronautics and Astronautics  > 2002  >  28(1): 4-7.
ZENG Jian-ping, CHENG Peng, ZHANG Li-junet al. Improved Solvable Condition for H∞ Control Problem via State Feedback[J]. Journal of Beijing University of Aeronautics and Astronautics, 2002, 28(1): 4-7. (in Chinese)
Citation: ZENG Jian-ping, CHENG Peng, ZHANG Li-junet al. Improved Solvable Condition for H∞ Control Problem via State Feedback[J]. Journal of Beijing University of Aeronautics and Astronautics, 2002, 28(1): 4-7. (in Chinese)
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Improved Solvable Condition for H∞ Control Problem via State Feedback

  • 1.

    Beijing University of Aeronautics and Astronautics, School of Automation Science and Electrical Engineering

  • 2. Beijing University of Aeronautics and Astronautics, Dept. of Computer Science and Engineering

  • Received Date: 28 Apr 2000
  • Publish Date: 31 Jan 2002
    Abstract
  • Simplified solvable condition for H∞ control problem via state feedback is considered. The solvability of H∞ control problem via state feedback is considered to be equivalent to that of a class of linear matrix inequality (LMI). It can reduce the variable dimension by deleting redundancy matrix variables for the class of LMI, and a dimension-reduced LMI is obtained then. Moreover, the feasible solution set to the former LMI can be reconstructed via that of the latter. On the above basis, an improved solvable condition for H∞ control problem via state feedback is deduced. The H∞ controller set can be constructed by the feasible solution to the simplified solvable condition, and it also has more plentiful free parameters. Finally, two simple examples are given to show the validity of this approach.

     

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    • References(1)
  • [1] 姜长生, 孙隆和, 吴庆宪,等. 系统理论与鲁棒控制[M]. 北京:航天工业出版社, 1998. [2]郭 雷, 忻 欣, 冯纯伯. 基于LMI的一种统一的降阶控制器设计方法[J]. 中国科学(E), 1997, 27(4):353~361. [3]郭 雷, 忻 欣, 冯纯伯. 基于LMI的一类混合H2/H∞控制问题的降阶控制器设计——连续情形[J]. 自动化学报, 1998, 24(3):294~299. [4]Iwasaki T, Skelton R E. All controllers for the general H∞ control problem:LMI existence conditions and state space formulas[J]. Automatica, 1994, 30(8):1307~1317.
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