International Journal of Control, Automation, and Systems

  • 제4권3호
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  • Pages.271-280
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  • 2006
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  • 1598-6446(pISSN)
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  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

An Improvement on Robust $H{\infty}$ Control for Uncertain Continuous-Time Descriptor Systems

  • Lee Hung-Jen (Department of Electrical and Electronics Engineering, National Kaohsiung University of Applied Science) ;
  • Kau Shih-Wei (Department of Electrical and Electronics Engineering, National Kaohsiung University of Applied Science) ;
  • Liu Yung-Sheng (Department of Electrical and Electronics Engineering, National Kaohsiung University of Applied Science) ;
  • Fang Chun-Hsiung (Department of Electrical and Electronics Engineering, National Kaohsiung University of Applied Science) ;
  • Chen Jian-Liung (Department of Electrical Engineering, National Sun Yat-Sen University) ;
  • Tsai Ming-Hung (Department of Electrical Engineering, National Sun Yat-Sen University) ;
  • Lee Li (Department of Electrical Engineering, National Sun Yat-Sen University)
  • 발행 : 2006.06.01
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초록

This paper proposes a new approach to solve robust $H{\infty}$ control problems for uncertain continuous-time descriptor systems. Necessary and sufficient conditions for robust $H{\infty}$ control analysis and design are derived and expressed in terms of a set of LMIs. In the proposed approach, the uncertainties are allowed to appear in all system matrices. Furthermore, a couple of assumptions that are required in earlier design methods are not needed anymore in the present one. The derived conditions also include several interesting results existing in the literature as special cases.

키워드

참고문헌

  1. B. Benkatasubramanian, 'On a singular transformation for analyzing the global dynamics of a class of singular DAE's,' Proc. of SINS'92, pp. 364-371, 1992
  2. J.-L. Chen, LMI Approach to Positive Real Analysis and Design for Descriptor Systems, Ph.D. Dissertation, National Sun Yat-Sen University, Taiwan, 2003
  3. L. Dai, Singular Control Systems - Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989
  4. C.-H. Fang and L. Lee, 'Stability robustness analysis of uncertain discrete-time descriptor systems,' Proc. of the 15th World Congress of IFAC, Barcelona, Spain, 2002
  5. K.-L. Hsiung and L. Lee, 'Lyapunov inequality and bounded real lemma for discrete-time descriptor systems,' IEE Proc., Control Theory Appl., vol. 146, no. 4, pp. 327-331, 1999 https://doi.org/10.1049/ip-cta:19990451
  6. J.-C. Hung, H.-S. Wang, and F.-R. Chang, 'Robust $H{\infty}$ control for uncertain linear timeinvariant descriptor systems,' IEE Proc. Control Theory Appl., vol. 147, no. 6, pp. 648-654, 2000
  7. T. Katayama, '(J,J')-spectral factorization and conjugation for discrete-time descriptor system,' Circ. System Signal Process, vol. 15, pp. 649-669, 1996 https://doi.org/10.1007/BF01188987
  8. A. Kawamoto and T. Katayama, 'Standard $H{\infty}$ control problem for descriptor systems,' Proc. of the 36th CDC, pp. 4130-4133, 1997
  9. A. Kumar and P. Daoutids, 'Feedback control of nonlinear differential-algebraic equation systems,' AIChE Journal, vol. 41, pp. 619-636, 1995 https://doi.org/10.1002/aic.690410319
  10. F. L. Lewis, 'A survey of linear singular systems,' J. Circuits, Systems, and Signal Processing, vol. 5, no. 1, pp. 3-36, 1986 https://doi.org/10.1007/BF01600184
  11. C. Lin, J. Wang, D. Wang, and C. B. Soh, 'Robustness of uncertain descriptor systems,' Systems and Control Letters, vol. 31, pp. 129-138, 1997 https://doi.org/10.1016/S0167-6911(97)00038-8
  12. D. G. Luenberger and A. Arbel, 'Singular dynamic Leontief systems,' Econometrica, vol. 45, pp. 991-994, 1977 https://doi.org/10.2307/1912686
  13. I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, '$H{\infty}$ control for descriptor systems: A matrix inequalities approach,' Automatica, vol. 33, no. 4, pp. 669-673, 1997 https://doi.org/10.1016/S0005-1098(96)00193-8
  14. R. W. Newcomb, 'The semistate description of nonlinear time variable circuits,' IEEE Trans. on Circuits Systems, vol. 28, no. 1, pp. 62-71, 1981 https://doi.org/10.1109/TCS.1981.1084908
  15. K. Takaba, N. Morihira, and T. Katayama, '$H{\infty}$ control for descriptor systems - a J-spectral factorization approach,' Proc. of the 33rd CDC, pp. 2251-2256, 1994
  16. M.-H. Tsai, J.-H. Chen, and L. Lee, 'Robust $H{\infty}$ control for uncertain continuous time descriptor systems,' Proc. of R.O.C. Automatic Control Conference, pp. 1367-1372, 2002
  17. A. Rehm and F. Allgower, 'An LMI approach towards $H{\infty}$ control of discrete-time descriptor systems,' Proc. of the ACC, Anchorage, USA, pp. 614-619, 2002
  18. H.-S. Wang, C.-F. Yung, and F.-R. Chang, 'Bound real lemma and $H{\infty}$ control for descriptor systems,' IEE Proc.-Control Theory Appl., vol. 145, no. 3, pp. 316-322, 1998 https://doi.org/10.1049/ip-cta:19982048
  19. L. Xie, 'Output feedback $H{\infty}$ control of systems with parameter uncertainty,' Int. J. Control, vol. 63, no. 4, pp. 741-750, 1996 https://doi.org/10.1080/00207179608921866
  20. S. Xu and C. Yang, '$H{\infty}$ state feedback control for discrete singular systems,' IEEE Trans. on Automatic Control, vol. 45, no. 7, pp. 1405-1409, 2000 https://doi.org/10.1109/9.867074