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Practical stability analysis and synthesis of linear descriptor systems with disturbances

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Abstract

This paper considers the problems of practical stability analysis and synthesis of linear descriptor systems subject to time-varying and norm-bounded exogenous disturbances. A sufficient condition for the systems to be regular, impulsive-free and practically stable is derived. Then the synthesis problem is addressed and a state feedback controller is designed. To deal with the computational issue, the conditions of the main results are converted into linear matrix inequality (LMI) feasibility problems. Furthermore, two optimization algorithms are formulated to improve the system performances. Finally, numerical examples are given to illustrate the obtained results.

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Author information

Authors and Affiliations

  1. Institute of Systems Science, Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang, 110004, PRC

    Chun-Yu Yang, Xin Jing, Qing-Ling Zhang & Lin-Na Zhou

Authors
  1. Chun-Yu Yang

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  2. Xin Jing

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  3. Qing-Ling Zhang

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  4. Lin-Na Zhou

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Corresponding author

Correspondence toQing-Ling Zhang.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60574011).

Chun-Yu Yang received B. Sc. degree from the Mathematics Department of Northeastern University, Shenyang, China in 2002. He is now a Ph.D. candidate at Northeastern University.

His research interests include descriptor systems, robust control, and fuzzy control.

Xin Jing received the B. Sc. degree from Applied Mathematics Department of Northeastern University, Shengyang, China, in 1995. She was a professor at Shenyang Jianzhu University. She is currently a Ph. D. candidate at Northeastern University.

Her research interests include optimization algorithm, positive real control theory, model order reduction for descriptor systems.

Qing-Ling Zhang received B. Sc. and M. Sc. degrees from the Mathematics Department and the Ph.D. degree from the Automatic Control Department of Northeastern University, Shenyang, China, in 1982, 1986, and 1995, respectively.

He finished his two-year postdoctoral work in Automatic Control Department of Northwestern Polytechnical University, Xi’an, China, in 1997. Since then, he has been a professor at Northeastern University. He is also a member of the University Teaching Advisory Committee of National Ministry of Education. He has published six books and more than 230 papers about control theory and applications. He received 14 prizes from central and local governments for his research. He also received the Golden Scholarship from Australia in 2000. He has visited Hong Kong University, Sydney University, Western Australia University and Niigata University, Pohan University of Science and Technology, Seoul University, Alberta University, Lakehead University and Wisor University as a research associate, research fellow, senior research fellow, and visiting professor, respectively.

His research interests include robust control, fuzzy control, and descriptor systems.

Lin-Na Zhou received B. Sc. degree from the Department of Water Conservancy Engineering of North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou, China in 2001 and the Ph.D. degree from College of Information Science and Engineering of Northeastern University, Shenyang, China in 2007.

Her research interests include descriptor systems, robust control, and fuzzy control.

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Yang, CY., Jing, X., Zhang, QL.et al. Practical stability analysis and synthesis of linear descriptor systems with disturbances.Int. J. Autom. Comput.5, 138–144 (2008). https://doi.org/10.1007/s11633-008-0138-4

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