International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Delay-dependent Stabilization for Systems with Multiple Unknown Time-varying Delays

  • Wu, Min (School of Information Science and Engineering, Central South University) ;
  • He, Yong (School of Information Science and Engineering, Central South University) ;
  • She, Jin-Hua (School of Bionics, Tokyo University of Technology)
  • Published : 2006.12.30
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Abstract

This paper deals with the delay-dependent and rate-independent stabilization of systems with multiple unknown time-varying delays and time-varying structured uncertainties. All the linear matrix inequalities based conditions are derived by employing free-weighting matrices to express the relationships between the terms in the Leibniz-Newton formula. The criteria do not require any tuning parameters. Numerical examples demonstrate the validity of the method.

Keywords

References

  1. E. Fridman and U. Shaked, 'Delay-dependent stability and $H_\infty$ control: Constant and timevarying delays,' Int. J. Control, vol. 76, no. 1, pp. 48-60, 2003 https://doi.org/10.1080/0020717021000049151
  2. P. Park, 'A delay-dependent stability criterion for systems with uncertain time-invariant delays,' IEEE Trans. on Automatic Control, vol. 44,no.4,pp. 876-877,1999 https://doi.org/10.1109/9.754838
  3. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, 'Delay-dependent robust stabilization of uncertain state-delayed systems,' Int. J. Control, vol. 74, no. 14, pp. 1447-1455, 2001 https://doi.org/10.1080/00207170110067116
  4. E. Fridman and U. Shaked, 'An improved stabilization method for linear time-delay systems,' IEEE Trans. on Automatic Control, vol. 47, no. 11, pp. 1931-1937,2002 https://doi.org/10.1109/TAC.2002.804462
  5. Q. L. Han, 'A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays,' Automatica, vol. 40, no. 10, pp. 1791-1796, 2004 https://doi.org/10.1016/j.automatica.2004.05.002
  6. X. J. Jing, D. L. Tan, and Y. C. Wang, 'An LMI approach to stability of systems with severe time-delay,' IEEE Trans. on Automatic Control, vol. 49, no. 7, pp. 1192-1195,2004 https://doi.org/10.1109/TAC.2004.831109
  7. H. Gao, J. Lam, C. Wang, and Y. Wang, 'Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay,' lEE Proc-Control Theory Appl., vol. 151, no.6,pp.69l-698,2004
  8. Y. S. Lee, Y. S. Moon, W. H. Kwon, and P. O. Park, 'Delay-dependent robust Hi; control for uncertain systems with a state-delay,' Automatica, vol. 40, no. 1, pp. 65-72,2004 https://doi.org/10.1016/j.automatica.2003.07.004
  9. Y. He, M. Wu, J.-H. She, and O. P. Liu, 'Delaydependent robust stability criteria for uncertain neutral systems with mixed delays,' Syst. Contr. Lett., vol. 51, no. 1, pp. 57-65,2004 https://doi.org/10.1016/S0167-6911(03)00207-X
  10. Y. He, M. Wu, J.-H. She, and O. P. Liu, 'Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopictype uncertainties,' IEEE Trans. on Automatic Control, vol. 49, no. 5, pp. 828-832, 2004 https://doi.org/10.1109/TAC.2004.828317
  11. M. Wu, Y. He, J.-H. She, and O. P. Liu, 'Delaydependent criteria for robust stability of timevarying delay systems,' Automatica, vol. 40, no. 8,pp.1435-1439, 2004 https://doi.org/10.1016/j.automatica.2004.03.004
  12. Y.-J. Sun, J.-G. Hsieh, and H.-C. Yang, 'On the stability of uncertain systems with multiple timevarying delays,' IEEE Trans. on Automatic Control, vol. 42, no. 1, pp. 101-105, 1997 https://doi.org/10.1109/9.553692
  13. Y. Y. Cao, Y. X. Sun, and C. W. Cheng, 'Delay-dependent robust stabilization of uncertain systems with multiple state delays,' IEEE Trans. on Automatic Control, vol. 43, no. 11, pp. 1608-1612, 1998 https://doi.org/10.1109/9.728880
  14. T. J. Su and C. O. Huang, 'Robust stability of delay dependence for linear uncertain systems,' IEEE Trans. on Automatic Control, vol. 37, no. 10, pp. 1656-1659, 1992 https://doi.org/10.1109/9.256406
  15. E. K. Boukas and N. F. Al-Muthairi, 'Delaydependent stabilization of singular linear systems with delays,' Int. J Innovative Computing, Information and Control, vol. 2, no. 2, pp. 283-291, 2006
  16. C. Lin, Q. O. Wang, and T. H. Lee, 'A less conservative robust stability test for linear uncertain time-delay systems,' IEEE Trans. on Automatic Control, vol. 51, no. 1, pp. 87-91, 2006 https://doi.org/10.1109/TAC.2005.861720
  17. K. Gu and S. I. Niculescu, 'Additional dynamics in transformed time delay systems,' IEEE Trans. on Automatic Control, vol. 45, no. 3, pp. 572-575, 2000 https://doi.org/10.1109/9.847747
  18. K. Gu and S. I. Niculescu, 'Further remarks on additional dynamics in various model transformations of linear delay systems,' IEEE Trans. on Automatic Control, vol. 46, no. 3, pp. 497 -500, 2001 https://doi.org/10.1109/9.911431
  19. I. R. Petersen and C. V. Hollot, 'A Riccati equation approach to the stabilization of uncertain linear systems,' Automatica, vol. 22, no. 4, pp. 397-411, 1986 https://doi.org/10.1016/0005-1098(86)90045-2
  20. L. Xie, 'Output feedback Hi; control of systems with parameter uncertainty,' Int. J. Control, vol. 63, no.4, pp. 741-750, 1996 https://doi.org/10.1080/00207179608921866
  21. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993
  22. S. Boyd, L. EL Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequality in System and Control Theory, Studies in Applied Mathematics, SIAM, Philadelphia, 1994