전기학회논문지 (The Transactions of The Korean Institute of Electrical Engineers)

  • 제65권3호
  • /
  • Pages.457-462
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  • 2016
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  • 1975-8359(pISSN)
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  • 2287-4364(eISSN)
대한전기학회 (The Korean Institute of Electrical Engineers)
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새로운 적분구간 비례 적분 부등식을 이용한 시간지연 선형시스템의 안정성

Stability of Time-delayed Linear Systems with New Integral Inequality Proportional to Integration Interval

  • Kim, Jin-Hoon (Dept. of Electrical and Computer Engineering, Chungbuk National University)
  • 투고 : 2015.10.30
  • 심사 : 2016.02.05
  • 발행 : 2016.03.01
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초록

In this paper, we consider the stability of time-delayed linear systems. To derive an LMI form of result, the integral inequality is essential, and Jensen's integral inequality was the best in the last two decades until Seuret's integral inequality is appeared recently. However, these two are proportional to the inverse of integration interval, so another integral inequality is needed to make it in the form of LMI. In this paper, we derive an integral inequality which is proportional to the integration interval which can be easily converted into LMI form without any other inequality. Also, it is shown that Seuret's integral inequality is a special case of our result. Next, based on this new integral inequality, we derive a stability condition in the form of LMI. Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

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참고문헌

  1. M. Wu, Y. He, J.-H. She and H.-P. Liu, "Delaydependent criteria for robust stability of time-varying delay system", Automatica, vol. 40, no. 8, pp. 1435-1439, 2004. https://doi.org/10.1016/j.automatica.2004.03.004
  2. Y. He, Q.-G. Wang, L. Xie and C. Lin, "Delay-rangedependent stability for systems with time-varying delay", Automatica, vol. 43, pp. 371-376, 2007. https://doi.org/10.1016/j.automatica.2006.08.015
  3. P. 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
  4. 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
  5. J.-H. Kim, "Note on stability of linear systems with time-varying delay", Automatica, vol. 47, pp. 2118-2121, 2011. https://doi.org/10.1016/j.automatica.2011.05.023
  6. P. Park, J.W. Ko and C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, vol. 47, pp. 235-238.
  7. A. Seuret and F. Gouaisbaut, "Wirtinger-based integral inequality: Application to time-delayed systems", Automatica, vol. 49, pp. 2860-2866, 2013. https://doi.org/10.1016/j.automatica.2013.05.030
  8. O.M. Kwon, M.J. Park, J.H. Park, S.M. Lee and E. J. Cha, "Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality, J. of the Franklin Institute, vol. 351, pp. 5382-5398, 2014.
  9. J.-H. Kim, "Further improvement of Jensen inequality and application to stability of time-delayed systems, Automatica, vol. 64, pp. 121-125, 2016. https://doi.org/10.1016/j.automatica.2015.08.025
  10. S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishhnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied mathematics, 1994.
  11. K. Gu, V. L. Kharitonov and J. Chen, Stability of time-delay systems, Birkhausser, 2003.