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A BMI approach for H 2 based decomposition

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  • Control Theory
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Abstract

The problem of static precompensator design for uncertain system to reduce the coupling is considered in this paper. Diagonal dominant is redefined using the H 2 norm of the system. Based on this definition, the necessary and sufficient conditions for system diagonal dominant, which are described by Linear Matrix Inequalities (LMIs), are derived. These conditions are extended to design static precompensator for both nominal system and uncertain system. The conditions are in the form of Bilinear Matrix Inequalities (BMIs), and the combined bisection and path-following algorithm is developed to solve the BMIs. An example is given to show the effectiveness of the proposed method.

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Authors and Affiliations

  1. Key Lab for Image Processing & Intelligent Control, Department of Control Science and Engineering, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, China

    Zhishen Wang, Lei Liu & Yongji Wang

  2. School of Aeronautics and Aerospace in Central South University, Changsha, China

    Dangjun Zhao

Authors
  1. Zhishen Wang
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  2. Lei Liu
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  3. Yongji Wang
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  4. Dangjun Zhao
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Corresponding author

Correspondence to Lei Liu.

Additional information

Recommended by Editorial Board member Izumi Masubuchi under the direction of Editor Zengqi Sun.

This work was supported in part by the National Nature Science Foundation of China (No.60975058), National High Technology Research and Development Program under grant (No.2008AA04Z207), National Nature Science Foundation of China (No.61075095) Nature Science Foundation of Hubei (No.2010CDB01904), 2010 Aerospace Technology Support Foundation, 2010 Defense Innovation Research Foundation of Huazhong University of Science and Technology, Fundamental Research Funds for the Central Universities (HUST: No. 2011QN148). The authors thank the anonymous reviewers for their valuable comments and suggestions.

Zhishen Wang received his B.S. degree in automation from Guangdong University of Technology, China in 2008. He is now a student at Department of Control Science and Engineering in Huazhong University of Science and Technology, China. His research interests include decoupling control and robust control.

Lei Liu received his Ph.D. degree in control theory and control engineering from Huazhong University of Science and Technology, China in 2009. He is now a lecturer at Department of Control Science and Engineering in Huazhong University of Science and Technology. His research interests include system modeling and fault tolerant control.

Yongji Wang received his Ph.D. degree in Power Plant Engineering from Huazhong University of Science and Technology, China in 1990. He is now a professor at Department of Control Science and Engineering in Huazhong University of Science and Technology. His research interests include neural network, system identification and control.

Dangjun Zhao received his Ph.D. degree in Control Engineering from Huazhong University of Science and Technology, China in 2011. He is now a lecturer in School of Aeronautics and Aerospace in Central South University, China. His research interests include nonlinear control and spacecrafts control.

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Wang, Z., Liu, L., Wang, Y. et al. A BMI approach for H 2 based decomposition. Int. J. Control Autom. Syst. 10, 470–480 (2012). https://doi.org/10.1007/s12555-012-0303-y

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  • DOI: https://doi.org/10.1007/s12555-012-0303-y

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