Journal of Electrical Engineering and Technology

The Korean Institute of Electrical Engineers (대한전기학회)
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New Stability Criteria for Linear Systems with Interval Time-varying State Delays

  • Kwon, Oh-Min (School of Electrical Engineering, Chungbuk National University) ;
  • Cha, Eun-Jong (Department of Biomedical Engineering, School of Medicine, Chungbuk National University)
  • Received : 2010.11.16
  • Accepted : 2011.05.17
  • Published : 2011.09.01
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Abstract

In the present paper, the problem of stability analysis for linear systems with interval time-varying delays is considered. By introducing a new Lyapunov-Krasovskii functional, new stability criteria are derived in terms of linear matrix inequalities (LMIs). Two numerical examples are given to show the superiority of the proposed method.

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References

  1. M. Kowsalya, K. K. Ray, Udai Shipurkar, and Saranathan, "Voltage Stability Enhancement by optimal placement of UPFC," J. Electri. Eng. & Tech., vol.4, no.3, pp.310-314, 2009. https://doi.org/10.5370/JEET.2009.4.3.310
  2. C. Subramani, Subhransu Sekhar Dash, M. Jagdeeshkumar and M. Arun Bhaskar, "Stability index based voltage collapse prediction and contingency analysis," J. Electri. Eng. & Tech., vol.4, no.4, pp.438−442, 2009. https://doi.org/10.5370/JEET.2009.4.4.438
  3. Mansour-Khalilian, Maghsoud-Mokhtari, Daryoosh- Nazarpour, and Behrouz-Tousi, "Transient stability enhancement by DSSC with fuzzy supplementary controller," J. Electri. Eng. & Tech., vol.5, no.3, pp.415−422, 2010. https://doi.org/10.5370/JEET.2010.5.3.415
  4. J. Raja, and C. Christober Asir Rajan, "Stability analysis and effect of CES and ANN based AGC for frequency excursion," J. Electri. Eng. & Tech., vol.5, no.4, pp.552−560, 2010. https://doi.org/10.5370/JEET.2010.5.4.552
  5. S.-I. Niculescu, Lecture Notes in Control and Information Sciences, Delay effects on stability: A robust control approach: London, Springer-Verlag, 2001.
  6. J.-P. Richard, "Time-delay systems: an overview of some recent advances and open problems," Automatica, vol. 39, pp. 1667-1694, 2003. https://doi.org/10.1016/S0005-1098(03)00167-5
  7. S. Xu, and J. Lam, "A survey of linear matrix inequality techniques in stability analysis of delay systems," Int. J. Syst. Sci., vol. 39, pp. 1095-1113, 2008. https://doi.org/10.1080/00207720802300370
  8. D. Yue, S. Won, and O. Kwon, "Delay dependent stability of neutral systems with time delay: an LMI Approach," IEE Proc.-Control Theory Appl., vol. 150, pp. 23-27, 2003. https://doi.org/10.1049/ip-cta:20030080
  9. P. G. Park, and J. W. Ko, "Stability and robust stability for systems with a time-varying delay," Automatica, vol. 43, pp. 1855-1858, 2007. https://doi.org/10.1016/j.automatica.2007.02.022
  10. O. M. Kwon, and J. H. Park, "On improved delaydependent robust control for uncertain time-delay systems," IEEE Trans. Autom. Control, vol. 49, pp. 1991-1995, 2004. https://doi.org/10.1109/TAC.2004.837563
  11. T. Li, L. Guo, and C. Lin, "A new criterion of delay-dependent stability for uncertain time-delay systems," IET Control Theory Appl., vol. 1, pp. 611-616, 2007. https://doi.org/10.1049/iet-cta:20060235
  12. Y. Ariba, and F. Gouaisbaut, "Delay-dependent stability analysis of linear systems with time-varying delay," in Proc. 46th IEEE Conf. on Decision and Control, pp.2053-2058, 2007.
  13. H. Shao, "New delay-dependent stability criteria for systems with interval delay," Automatica, vol. 45, pp. 744-749, 2009. https://doi.org/10.1016/j.automatica.2008.09.010
  14. J. Sun, G. P. Liu, J. Chen, and D. Rees, "Improved delay-range-dependent stability criteria for linear systems with time-varying delays," Automatica, vol. 46, pp. 466-470, 2010. https://doi.org/10.1016/j.automatica.2009.11.002
  15. X.-L. Zhu, Y. Wang, and G.-H. Yang, "New stability criteria for continuous-time systems with interval time-varying delay," IET COntrol Theory Appl., vol. 4, pp.1101-1107, 2010. https://doi.org/10.1049/iet-cta.2009.0176
  16. K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. 39th IEEE Conf. on Decision and Control, pp. 2805-2810, 2000.
  17. S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in systems and control Theory: Philadelphia, SIAM, 1994.
  18. R. E. Skelton, T. Iwasaki, and K. M. Grigoradis, A unified algebraic approach to linear control design: New York, Taylor and Francis, 1997.

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