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Improved LMI representations for delay-independent and delay-dependent stability conditions

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Abstract

Some new linear matrix inequality (LMI) representations for delay-independent and delay-dependent stability conditions are obtained by introducing additional matrices and eliminating the product coupling of the system matrices and the Lyapunov matrices. The results improve conservativeness of the given conditions for the analysis and the design of time-delay systems with polytopic-type uncertainty.

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References

  1. J. R. Zhang, C. R. Knopse, P. Tsiotras, Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions, IEEE Trans, on Automatic Control, Vol.46, No. 3, pp.482 - 486, 2001.

    Article  MATH  Google Scholar 

  2. X. Li, C. E. de Souza, Robust stabilization and H∞ control of uncertain linear time-delay systems, 13 th IFAC World Congress, San Francisco,USA.pp. 113 - 118,1996.

  3. L. Dugard, E. I. Verriest (Eds) , Stability and Control of Time-Delay Systems, Springer, 1997.

  4. S. Boyd, L. E. Ghaoui, E.Feron, V. Balakrishnan, Linear matrix inequality in systems and control theory, SIAM Frontier Series, SIAM, Philadelpha, PA, 1994.

    Google Scholar 

  5. P. Gahinet, P. Apkarian, A linear matrix inequality approach to H∞ Control, Int. J. Robust Nonlinear Control, Vol.4, No.5, pp.421 -448,1994.

    Article  MATH  Google Scholar 

  6. R. E. Skelton, T. Iwasaki, K. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, Taylor & Francis publishers, London, 1998.

    Google Scholar 

  7. Y. Ebihara, T. Hagjwara, New dilated LMI characterizations for continuous-time control design and robust multiobjective control, Proc. of the American Control Conf., Anchorage, AK, pp. 47 - 52,2002.

  8. Y. Ebihara, T. Hagiwara, Robust controller synthesis with parameter-dependent Lyapunov variables : A dilated LMI approach, Proc. of the 41 st IEEE Conf. on Decision and Control, Las Vegas, Nevada, pp. 4179-4184,2002.

  9. Y. Ebihara, T. Hagiwara, A Dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems, Proc. of the American Control Conf., Denver, Colorado, pp.839 - 844,2003.

  10. M. C. de Oliveira, J. Bemussou, J. C. Geromel, A new discretetime robust stability condition, Systems & Control Letters, Vol. 37, No.3, pp.261–265,1999.

    Article  MATH  Google Scholar 

  11. P. Apkarian, H. D. Tuan, J. Bernussou, Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) Characteristics, IEEE Trans, on Automatic Control, Vol.46, No.12, pp. 1941 -1946,2001.

    Article  MATH  Google Scholar 

  12. 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.

    Article  MATH  Google Scholar 

  13. Yingmin Jia, Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: A predictive approach, IEEE Trans, on Automatic Control, Vol.48, No.8, pp. 1413 - 1416,2003.

    Article  Google Scholar 

  14. Yingmin Jia, H. Kokame, J.Lunze, Simultaneous adaptive decoupling and model matching control of a fluidized bed combustor for sewage sludge, IEEE Trans. on Control Systems Technology, Vol.11, No. 4, pp.571–577,2003.

    Article  Google Scholar 

  15. E. Fridman, U. Shaked, A descriptor system approach to H∞ control of linear time-delay systems, IEEE Trans. on Automatic Control, Vol.47, No.2, pp.253–270,2002.

    Article  Google Scholar 

  16. E. Fridman, U. Shaked, An improved stabilization method for linear time-delay systems, IEEE Trans. on Automatic Control, Vol. 47, No. 11, pp. 1931–1937,2002.

    Article  Google Scholar 

  17. S. H. Esfahani, I. R. Petersen, An LMI approach to output-feedback guaranteed cost control for uncertain time-delay systems, Int. Journal of Robust Nonlinear Control, Vol. 10, No. 2, pp. 157 - 174,2002.

    Google Scholar 

  18. X. Li, C. E. de Souza, Criteria for robust stability and stabilization of uncertain linear system with state delay, Automatica, Vol.33, No.9, pp.1657–1662,1997.

    Article  Google Scholar 

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Authors and Affiliations

  1. The Seventh Research Division, BeiHang University, 100083, Beijing, China

    Yingmin Jia

  2. Department of Electrical & Electronic Systems, Osaka Prefecture University, Gakuen-cho 1 — 1, Sakai, 599 — 8531, Osaka, Japan

    Hideki Kokame

Authors
  1. Yingmin Jia
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  2. Hideki Kokame
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Additional information

This work was supported by the National Natural Science Foundation of China (60374001, 60334030), by the Chinese Ministry of Education (20030006003), and by the Japan Society for the Promotion of Science.

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Jia, Y., Kokame, H. Improved LMI representations for delay-independent and delay-dependent stability conditions. J. Control Theory Appl. 1, 70–76 (2003). https://doi.org/10.1007/s11768-003-0011-5

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  • DOI: https://doi.org/10.1007/s11768-003-0011-5

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