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Delay-dependent criteria for the robust stability of systems with time-varying delay

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Abstract

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.

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References

  1. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.

    MATH  Google Scholar 

  2. T. J. Su, C. G. Huang, Robust stability of delay dependence for linear uncertain systems, IEEE Trans. on Automatic Control, Vol. 37, No. 10, pp.1656–1659,1992.

    Article  MATH  Google Scholar 

  3. Y. Y. Cao, Y. X. Sun, 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.

    Article  MATH  Google Scholar 

  4. 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.

    Article  MATH  Google Scholar 

  5. Y. S. Moon, P. Park, W. H. Kwon, Y. S. Lee, Delay-dependent robust stabilization of uncertain state-delayed systems, Int. J. Control, Vol. 74, No. 14, pp. 1447 - 1455,2001.

    Article  MATH  Google Scholar 

  6. J. H. Kim, Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty, IEEE Trans, on Automatic Control, Vol.46, No.5, pp.789 - 792,2001.

    Article  MATH  Google Scholar 

  7. D. Yue, S. Won, An improvement on 'Delay and its time-derivative dependent roubst stability of time-delayed linear systems with uncertainty, IEEE Trans, on Automatic Control, Vol.47, No.2, pp.407- 408,2002.

    Article  Google Scholar 

  8. J. H. Lee, S. W. Kim, W. H. Kwon, Memoryless H∞ controllers for state delayed systems, IEEE Trans, on Automatic Control, Vol. 39, No.l, pp. 159–162,1994.

    Article  MATH  Google Scholar 

  9. H. G. Chen, K. W. Han, Improved quantitative measures of robustness for multivariable systems, IEEE Trans. on Automatic Control, Vol.39, No.4, pp.807 - 810,1994.

    Article  MATH  Google Scholar 

  10. B. G. Xu, Stability robustness bounds for linear systems with multiple time-varying delayed perturbations, Int. J. Sys. Sci., Vol.42, No.12, pp.1311–1317,1997.

    Article  Google Scholar 

  11. H. Trinh, M. Aldeen, On robustness and stabilization of linear systems with delayed nonlinear perturbations. IEEE Trans. on Automatic Control, Vol.42, No.7, pp.1005 - 1007,1997.

    Article  MATH  Google Scholar 

  12. Y. Y. Cao, J. Lam, Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations. Int. J. Sys. Sci., Vol.31, No.3, pp. 359 - 365,2000.

    Article  MATH  Google Scholar 

  13. M. L. Ni, M. J. Er, Stability of linear systems with delayed perturbations: an LMI approach, IEEE Trans. on Circuits Systems I, Vol.49, No.l, pp.108 - 112,2002.

    Google Scholar 

  14. A. Goubet-Bartholomeus, M. Dambrine, Stability of perturbed systems with time-varying delays, Systems & Control Lettels, Vol.31, No.3, pp.155 - 163,1997.

    Article  Google Scholar 

  15. S. Boyd, L. Ei. Ghaoui, E. Feron, et al, Linear matrix inequality in system and control theory. Studies in Applied Mathematics, SIAM, Philadelphia, Vol.15, 1994.

    Google Scholar 

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, 410083, Changsha Hunan, China

    Min Wu & Yong He

  2. School of Mathematical Science and Computing Technology, Central South University, 410083, Changsha Hunan, China

    Yong He

  3. Department of Mechatronics, Tokyo University of Technology, 192-0982, Tokyo, Japan

    Jinhua She

Authors
  1. Min Wu
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  2. Yong He
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  3. Jinhua She
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Additional information

This work was supported by the Doctor Subject Foundation of China (No. 2000053303).

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Wu, M., He, Y. & She, J. Delay-dependent criteria for the robust stability of systems with time-varying delay. J. Control Theory Appl. 1, 97–100 (2003). https://doi.org/10.1007/s11768-003-0016-0

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  • DOI: https://doi.org/10.1007/s11768-003-0016-0

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