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

The Korean Institute of Electrical Engineers (대한전기학회)
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Delay-dependent Robust Stability of Uncertain Dynamic Systems with Time-varying Delays

시변 지연이 존재하는 불확실 동적 시스템의 지연 의존 강인 안정성

  • 권오민 (충북대학교 전기공학과) ;
  • 박주현 (영남대학교 전기공학과)
  • Published : 2009.01.01
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Abstract

In this paper, the stability analysis for uncertain dynamic systems with time-varying delays is considered. By constructing a new Lyapunov functional, a novel stability criterion is established in terms of linear matrix inequalities (LMIs). Two numerical examples are carried out to support the effectiveness of the proposed method.

Keywords

References

  1. J. Hale, and S.M.V. Lunel, Introduction to Functional Differential Equatins, Springer-Verlag, New York, 1993
  2. V.B. Kolmanovskii, and A. Myshkis, Applied Theory to Functional Differential Equations, Kluwer Academic Publishers, Boston, 1992
  3. J.H. Park, S. Won, 'Asymptotic stability of neutral systems with multiple delays', Journal of Optimization Theory and Applications, vol. 103, pp.187-200, 1999
  4. O.M. Kwon, Ju H. Park, S.M. Lee, 'On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays', Applied Mathematics and Computations, vol.197, pp.864-873, 2008 https://doi.org/10.1016/j.amc.2007.08.048
  5. Q.-L. Han, 'Robust stability of uncertain delay-differential systems of neutral type', Automatica, vol.38, pp.719-723, 2002 https://doi.org/10.1016/S0005-1098(01)00250-3
  6. S. Xu, J. Lam, Y. Zou, 'Further results on delay-dependent robust stability conditions of uncertain neutral systems', International Journal of Robust and Nonlinear Control, vol.15, pp.233-246, 2005 https://doi.org/10.1002/rnc.983
  7. M. Wu, Y. He, J-H. She, 'New delay-dependent stability criteria and stabilizing method for neutral systems', IEEE Transactions on Automatic Control, vol.49, pp.2266-2271, 2004 https://doi.org/10.1109/TAC.2004.838484
  8. S. Xu, J. Lam, 'Improved delay-dependent stability criteria for time-delay systems', vol.50, pp.384-387, 2005 https://doi.org/10.1109/TAC.2005.843873
  9. Y. He, M. Wu, J.-H. She, G.-P. Liu, 'Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties' , IEEE Transactions on Automatic Control, vol.49, pp.828-832, 2004 https://doi.org/10.1109/TAC.2004.828317
  10. P. Park, 'A delay-dependent stability criterion for system with uncertain time-invarient delays', IEEE Transactions on Automatic Control, vol. 44, No. 11, pp.876-877, 2004
  11. J. -H. Kim, 'Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty', IEEE Transactions on Automatic Control, vol.46, pp.789-792, 2001 https://doi.org/10.1109/9.920802
  12. D. Yue and S. Won, 'An improvement on delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty', IEEE Transactions on Automatic Control, vol.47, pp.407-408, 2002 https://doi.org/10.1109/9.983390
  13. E. Fridman and U. Shaked, 'A descriptor system approach to $\text H_\infty$ control of linear time-delay systems', IEEE Transactions on Automatic Control, vol.44, pp.253-270, 2002
  14. X.-J Jing, D.-L. Tian, and Y.-C. Wang, 'An LMI approach to stability of systems with severe time-delay', IEEE Transactions on Automatic Control, vol.49, pp.1192-1195, 2004 https://doi.org/10.1109/TAC.2004.831109
  15. O.M. Kwon, and J.H. Park, 'An improved delay-dependent robust control for uncertain time-delay systems', IEEE Transactions on Automatic Control, vol. 49, No. 11, pp.1991-1995, 2004 https://doi.org/10.1109/TAC.2004.837563
  16. Y. He, M. Wu, J.-H. She, 'Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays', Systems and Control Letters, vol.51 , pp.57 -65, 2004 https://doi.org/10.1016/S0167-6911(03)00207-X
  17. J.-H. Kim, Y.-G. Yi, 'Delay-dependent robust stability of uncertain time-delayed linear systems', Trans. KIEE, 55D, pp.147-156, 2006
  18. M.N.A. Parlakci, 'Robust stability of uncertain time-varying state-delayed systems', IEE Proceedings-Control Theory and Applications, vol.153, pp.469-477, 2006 https://doi.org/10.1049/ip-cta:20050099
  19. C. Peng and Y.-C. Tian, 'Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay', Journal of Computational and Applied Mathematics, vol.214, pp.480-494, 2008 https://doi.org/10.1016/j.cam.2007.03.009
  20. S. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Philadelphia, SIAM, 1994
  21. P. Gahinet, A. Nemirovski, A. Laub, M. GChilali, LMI Control Toolbox User's Guide, The Mathworks, Natick, Massachusetts, 1995
  22. X. Jiang, Q.L. Han, New stability criteria for linear systems with interval time-varying delay, Automatica, vol.44, pp.2680-2685, 2008 https://doi.org/10.1016/j.automatica.2008.02.020