Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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An LMI-based Decentralized Sliding Mode Control Design Method for Large Scale Systems

대규모 시스템을 위한 LMI기반 비집중화 슬라이딩 모드 제어기 설계

  • 최한호 (동국대학교 전기공학과)
  • Published : 2005.08.01
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Abstract

In this paper, we consider the problem of designing decentralized sliding mode control laws far a class of large scale systems with mismatched uncertainties. We derive a sufficient condition far the existence of a linear switching surface in terms of a linear matrix inequalities(LMIs), and we parameterize the linear switching surfaces in terms of the solution matrices to the given LMI existence conditions. We also give an algorithm for designing decentralized switching feedback control laws. Finally, we give a design example in order to show the effectiveness of our method.

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References

  1. R. A. DeCarlo, S. H. Zak, and G. P. Matthews, 'Variable structure control of nonlinear multivariable systems: A Tutorial', Proceedings of IEEE, vol. 76, no. 3, pp. 212-232, 1988 https://doi.org/10.1109/5.4400
  2. O. M. E. ElGhezawi, A. S. I. Zinober, and S. A. Billings, 'Analysis and design of variable structure systems using a geometric approach,' Int. J. Contr., vol. 38, pp.657-671, 1983 https://doi.org/10.1080/00207178308933100
  3. V. I. Utkin, 'Variable Structure Systems with Sliding Modes', IEEE Trans. Automat. Contr., vol. AC-22, No.2, pp. 212-222, 1977 https://doi.org/10.1109/TAC.1977.1101446
  4. H. Khurana, S. I. Ahson and S. S. Lamba, 'On stabilization of large-scal control systems using variable structure system theory' IEEE Trans. Automat. Contr., vol. 31, pp.176-178, 1986 https://doi.org/10.1109/TAC.1986.1104203
  5. G. P. Matthews and R. A. DeCarlo, 'Decentralized variable structure control of interconnected multiinput/multioutput nonlinear systems' Circuits Systems Sugnal Process, vol. 6, pp.363-387, 1987 https://doi.org/10.1007/BF01600000
  6. G. P. Matthews and R. A. DeCarlo, 'Decentralized tracking for a class of interconnected nonlinear systems using variable structure control' Automatica, vol. 24, pp.187-193, 1988 https://doi.org/10.1016/0005-1098(88)90027-1
  7. X. Xu, Y. Wu and W. Huang, 'Variable structure control approach of decentralized model reference adaptive systems,' IEE Proc. Pt. D, vol. 137, pp.302-306, 1990 https://doi.org/10.1049/ip-d.1990.0037
  8. P. Gahinet, A. Nemirovski and A. J. Laub, LMI Control Toolbox User's Guide, Natic, MA : The MathWorks Inc., 1995
  9. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in system and Control Theory, Philadelphia, SIAM, 1994
  10. C. Scherer, P. Gahinet, and M. Chilali, 'Multiobjective output-feedback control via LMI optimization,' IEEE Trans. Automat. Control., vol. 42, no. 7, pp. 896-911, 1993 https://doi.org/10.1109/9.599969
  11. D. Peaucelle, D. Arzelier, O. Bachelier and J. Bernussou, 'A new robust D-stability condition for real convex polytopic uncertainty,' Sytems & Control Letters, vol. 40, pp.21-30, 2000 https://doi.org/10.1016/S0167-6911(99)00119-X
  12. L. Xie and C. E. DeSouza, 'Robust $H_{\infty}$ control for linear systems with norm-bounded time-varying uncertainty,' IEEE Trans. Automat. Contr., vol. 37, pp.1188-1191 https://doi.org/10.1109/9.151101