Advanced SearchSearch Tips
Stability of Time-delayed Linear Systems with New Integral Inequality Proportional to Integration Interval
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Stability of Time-delayed Linear Systems with New Integral Inequality Proportional to Integration Interval
Kim, Jin-Hoon;
  PDF(new window)
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.
Stability;Time-delay;Proportional to integration interval;Integral inequality;LMI;
 Cited by
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. crossref(new window)

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. crossref(new window)

P. Park and J. W. Ko, "Stability and robust stability for systems with a time-varying delay, Automatica, vol. 43, pp. 1855-1858, 2007. crossref(new window)

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. crossref(new window)

J.-H. Kim, "Note on stability of linear systems with time-varying delay", Automatica, vol. 47, pp. 2118-2121, 2011. crossref(new window)

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.

A. Seuret and F. Gouaisbaut, "Wirtinger-based integral inequality: Application to time-delayed systems", Automatica, vol. 49, pp. 2860-2866, 2013. crossref(new window)

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.

J.-H. Kim, "Further improvement of Jensen inequality and application to stability of time-delayed systems, Automatica, vol. 64, pp. 121-125, 2016. crossref(new window)

S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishhnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied mathematics, 1994.

K. Gu, V. L. Kharitonov and J. Chen, Stability of time-delay systems, Birkhausser, 2003.