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Volume 12 Issue 2
April  2015
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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. https://doi.org/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. https://doi.org/10.1007/s11633-014-0868-4
shu

Bounded Real Lemmas for Fractional Order Systems

doi: 10.1007/s11633-014-0868-4

  • Department of Automation, University of Science and Technology of China, Hefei 230027, China;

  • School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Australia

Funds:

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

  • Received Date: 2012-07-29
  • Rev Recd Date: 2014-04-24
  • Publish Date: 2015-04-01
    Abstract
  • 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.

     

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