International Journal of Control, Automation, and Systems

  • 제6권2호
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  • Pages.263-268
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  • 2008
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  • 1598-6446(pISSN)
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  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

Improved Delay-independent $H_2$ Performance Analysis and Memoryless State Feedback for Linear Delay Systems with Polytopic Uncertainties

  • Xie, Wei (College of Automation Science and Technology, South China University of Technology)
  • 발행 : 2008.04.30
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초록

An improved linear matrix inequality (LMI) representation of delay-independent $H_2$ performance analysis is introduced for linear delay systems with delays of any size. Based on this representation we propose a new $H_2$ memoryless state feedback design. By introducing a new matrix variable, the new LMI formulation enables us to parameterize memoryles s controllers without involving the Lyapunov variables in the formulations. By using a parameter-dependent Lyapunov function, this new representation proposed here provides us the results with less conservatism.

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참고문헌

  1. J. Dolye, "Guaranteed margins for LQG regulators," IEEE Trans. on Automatic Control, vol. 23, pp. 756-757, 1978 https://doi.org/10.1109/TAC.1978.1101812
  2. J. Dolye, K. Zhou, K. Glover, and B. Francis, "State-space solutions to standard $H_2$ and $H^[\infty}$ problems," IEEE Trans. on Automatic Control, vol. 34, pp .831-847, 1989 https://doi.org/10.1109/9.29425
  3. K. Zhou, J. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1995
  4. S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies In Applied Mathematics, SIAM, Philadelphia, PA, 1994
  5. P. P. Khargonekar, I. R. Petersen, and K. Zhou, "Robust stabilization of uncertain linear systems: Quadratic stability and $H^[\infty}$ control theory," IEEE Trans. on Automatic Control, vol. 35, pp. 356-361, 1990 https://doi.org/10.1109/9.50357
  6. P. P. Khargonekar and M. A. Rotea, "Mixed $H_2/H^[\infty}$ control: A convex optimization approach," IEEE Trans. on Automatic Control, vol. 36, pp. 824-837, 1991 https://doi.org/10.1109/9.85062
  7. A. A. Stoorvogel, "The robust H2 control problem: A worst-case design," IEEE Trans. on Automatic Control, vol. 38, pp. 1358-1370, 1993 https://doi.org/10.1109/9.237647
  8. J. C. Geromel, M. C. de Oliveira, and L. Hsu, "LMI characterization of structure and robust stability," Linear Algebra and Its Applications, vol. 285, no. 1-3, pp. 69-80, 1998
  9. M. C. Oliveira, J. Bernussou, and J. C. Geromel, "A new discrete-time robust stability condition," Systems & Control Letters, vol. 37, pp. 261-265, 1999 https://doi.org/10.1016/S0167-6911(99)00035-3
  10. J. C. Geromel and J. Bernussou, "Extended H2 and H$\infty$ norm characterizations and controller parametrizations for discrete-time systems," International Journal of Control, vol. 75, pp. 666-679, 2002 https://doi.org/10.1080/00207170210140212
  11. U. Shaked, "Improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty," IEEE Trans. on Automatic Control, vol. 46, no. 4, pp. 652-656, 2001 https://doi.org/10.1109/9.917671
  12. Y. Jia, "Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainity: A prediction approach," IEEE Trans. on Automatic Control, vol. 48, no. 8, pp. 1413-1416, 2003 https://doi.org/10.1109/TAC.2003.815033
  13. Y. Ebihara and T. Hagiwara, "New dilated LMI characterizations for continuous-time multiobjective controller synthesis," Automatica, vol. 40, pp. 2003-2009, 2004 https://doi.org/10.1016/j.automatica.2004.06.009
  14. W. Xie, "H2 gain scheduled state feedback for LPV system with new LMI formulation," IEE Proceedings - Control Theory and Applications, vol. 152, no. 6, pp. 693-697, 2005 https://doi.org/10.1049/ip-cta:20050052
  15. E. Fridman and U. Shaked, "A descriptor system approach to H$\infty$ control of linear time-delay systems," IEEE Trans. on Automatic Control, vol. 47, pp. 253-270, 2002 https://doi.org/10.1109/9.983353
  16. M. C. Oliveira, J. Bernussou, and J. C. Geromel, "Synthesis of non-rational controllers for linear delay systems," Automatica, vol. 40, pp. 171-188, 2004 https://doi.org/10.1016/j.automatica.2003.09.004
  17. H. J. Gao, P. Shi, and J. L. Wang, "Parameterdependent robust stability of uncertain timedelay systems," Journal of Computational and Applied Mathematics, vol. 206, no. 1, pp. 366-373, 2007 https://doi.org/10.1016/j.cam.2006.07.027
  18. H. J. Gao, C. H. Wang, and J. L. Wang, "On H$\infty$ performance analysis for continuous-time stochastic systems with polytopic uncertainties," Circuits, Systems and Signal Processing, vol. 24, no. 4, pp. 415-429, 2005 https://doi.org/10.1007/s00034-004-0915-4
  19. H. J. Gao, J. Lam, L. H. Xie, and C. H. Wang, "New approach to mixed H2/H$\infty$ filtering for polytopic discrete-time systems," IEEE Trans. on Signal Processing, vol. 53, no. 8, pp. 3183-3192, 2005 https://doi.org/10.1109/TSP.2005.851116
  20. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox for Use with Matlab, Use's Guide, The Math Works Inc., Natick, MA, USA, 1995