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Frequency domain criteria for robust D-stability of mimo systems based on LMI method

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Abstract

The problem of checking robust D-stability of multi-in and multi-out (MIMO) systems was studied. Three system models were introduced, i.e. multilinear polynomial matrix, polytopic polynomial matrix and feedback system model. Furthermore, the convex property of each model with respect to the parametric uncertainties was estabilished respectively. Based on this, sufficient conditions for D-stability were expressed in terms of linear matrix inequalities (LMIs) involving only the convex vertices. Therefore, the robust D-stability was tested by solving an LMI optimal problem.

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Authors and Affiliations

  1. Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, P. R. China

    Li Hai-bin  (李海滨) (Doctor) & Wang Long  (王龙)

  2. Department of Applied Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China

    Wang Zhi-zhen  (王志珍)

  3. P. O. Box 1303-15, Beijing, 100073, P. R. China

    Li Hai-bin  (李海滨) (Doctor) & Li Zhao-ping  (李兆平)

  4. P. O. Box 53-601, Lanzhou, 730070, P. R. China

    Li Er-xiao  (李尔效)

Authors
  1. Li Hai-bin  (李海滨)
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  2. Wang Zhi-zhen  (王志珍)
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  3. Wang Long  (王龙)
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  4. Li Zhao-ping  (李兆平)
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  5. Li Er-xiao  (李尔效)
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Corresponding author

Correspondence to Li Hai-bin  (李海滨).

Additional information

Project supported by Post-Doctoral Science Foundation of China

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Li, Hb., Wang, Zz., Wang, L. et al. Frequency domain criteria for robust D-stability of mimo systems based on LMI method. Appl Math Mech 27, 207–213 (2006). https://doi.org/10.1007/s10483-006-0208-y

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  • DOI: https://doi.org/10.1007/s10483-006-0208-y

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