Bounded Real Lemmas for Fractional Order Systems

Shu Liang Yi-Heng Wei Jin-Wen Pan Qing Gao Yong Wang

Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao, Yong Wang. Bounded Real Lemmas for Fractional Order Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2015, 12(2): 192-198. doi: 10.1007/s11633-014-0868-4
引用本文: Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao, Yong Wang. Bounded Real Lemmas for Fractional Order Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2015, 12(2): 192-198. doi: 10.1007/s11633-014-0868-4
Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao and Yong Wang. Bounded Real Lemmas for Fractional Order Systems. International Journal of Automation and Computing, vol. 12, no. 2, pp. 192-198, 2015 doi:  10.1007/s11633-014-0868-4
Citation: Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao and Yong Wang. Bounded Real Lemmas for Fractional Order Systems. International Journal of Automation and Computing, vol. 12, no. 2, pp. 192-198, 2015 doi:  10.1007/s11633-014-0868-4

Bounded Real Lemmas for Fractional Order Systems

doi: 10.1007/s11633-014-0868-4
基金项目: 

This work was supported by National Natural Science Foundation of China (Nos. 61004017 and 60974103).

详细信息
    作者简介:

    Shu Liang received the B. Eng. degree in automation from University of Science and Technology of China (USTC), China in 2010. He is currently a Ph. D. candidate at USTC. His research interests include fractional order system stability analysis, controls and approximations, and robust control. E-mail: shuliang@mail.ustc.edu.cn ORCID iD: 0000-0002-9719-1987;Yi-Heng Wei received the B. Eng. de-gree in automation from Northeastern Uni-versity, China in 2010. He is currently a Ph. D. candidate at University of Science and Technology of China, China. His research interests include fractional order system identifications and controls. E-mail: neudawei@mail.ustc.edu.cn;Jin-Wen Pan received the B. Eng. de-gree in automation from University of Sci-ence and Technology of China, China in 2011. He is currently a Ph. D. candidate at USTC. His research interests include fractional order system, active disturbance rejection control and characteristic modelling theory. E-mail: panwen@mail.ustc.edu.cn;Qing Gao received the B. Eng. and Ph. D. degrees in mechanical and electrical engineering from the University of Science and Technology of China, China in 2008 and 2013, respectively. He also received the Ph. D. degree in mechatronics engineer-ing from the City University of Hong Kong, China in 2013. Since 2014, he has been with the School of Engineering and Information Technology, University of New South Wales, Canberra at the Australian Defence Force Academy, as a postdoctoral research associate. He was the recipient of the Chinese Academy of Sci-ences Presidential Scholarship (Special Prize) in 2013. He was also the recipient of the Outstanding Research Thesis Award from City University of Hong Kong in 2013. His research interests include quantum control, intelligent sys-tems and control, and variable structure control. E-mail: qing.gao@adfa.edu.au;

Bounded Real Lemmas for Fractional Order Systems

Funds: 

This work was supported by National Natural Science Foundation of China (Nos. 61004017 and 60974103).

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出版历程
  • 收稿日期:  2012-07-29
  • 修回日期:  2014-04-24

Bounded Real Lemmas for Fractional Order Systems

doi: 10.1007/s11633-014-0868-4
    基金项目:

    This work was supported by National Natural Science Foundation of China (Nos. 61004017 and 60974103).

    作者简介:

    Shu Liang received the B. Eng. degree in automation from University of Science and Technology of China (USTC), China in 2010. He is currently a Ph. D. candidate at USTC. His research interests include fractional order system stability analysis, controls and approximations, and robust control. E-mail: shuliang@mail.ustc.edu.cn ORCID iD: 0000-0002-9719-1987;Yi-Heng Wei received the B. Eng. de-gree in automation from Northeastern Uni-versity, China in 2010. He is currently a Ph. D. candidate at University of Science and Technology of China, China. His research interests include fractional order system identifications and controls. E-mail: neudawei@mail.ustc.edu.cn;Jin-Wen Pan received the B. Eng. de-gree in automation from University of Sci-ence and Technology of China, China in 2011. He is currently a Ph. D. candidate at USTC. His research interests include fractional order system, active disturbance rejection control and characteristic modelling theory. E-mail: panwen@mail.ustc.edu.cn;Qing Gao received the B. Eng. and Ph. D. degrees in mechanical and electrical engineering from the University of Science and Technology of China, China in 2008 and 2013, respectively. He also received the Ph. D. degree in mechatronics engineer-ing from the City University of Hong Kong, China in 2013. Since 2014, he has been with the School of Engineering and Information Technology, University of New South Wales, Canberra at the Australian Defence Force Academy, as a postdoctoral research associate. He was the recipient of the Chinese Academy of Sci-ences Presidential Scholarship (Special Prize) in 2013. He was also the recipient of the Outstanding Research Thesis Award from City University of Hong Kong in 2013. His research interests include quantum control, intelligent sys-tems and control, and variable structure control. E-mail: qing.gao@adfa.edu.au;

摘要: This paper derives the bounded real lemmas corresponding to L norm and H norm (L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality (LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-Yakubovich-Popov (KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism. However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.

English Abstract

Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao, Yong Wang. Bounded Real Lemmas for Fractional Order Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2015, 12(2): 192-198. doi: 10.1007/s11633-014-0868-4
引用本文: Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao, Yong Wang. Bounded Real Lemmas for Fractional Order Systems[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2015, 12(2): 192-198. doi: 10.1007/s11633-014-0868-4
Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao and Yong Wang. Bounded Real Lemmas for Fractional Order Systems. International Journal of Automation and Computing, vol. 12, no. 2, pp. 192-198, 2015 doi:  10.1007/s11633-014-0868-4
Citation: Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao and Yong Wang. Bounded Real Lemmas for Fractional Order Systems. International Journal of Automation and Computing, vol. 12, no. 2, pp. 192-198, 2015 doi:  10.1007/s11633-014-0868-4
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