83
Views
37
CrossRef citations to date
0
Altmetric
Original Articles

New results for delay-dependent stability of linear systems with time-varying delay

Pages 213-228 | Published online: 26 Nov 2010

  • BOYD , S. , EL GHAOUI , L. , FERON , E. and BALAKRISHNAN , V. 1994 . Linear Matrix Inequalities in Systems and Control Theory , Philadelphia : SIAM .
  • GAHINET , P. , NEMIROVSKI , A. , LAUB , A. J. and CHILALI , M. 1995 . LMI Control Toolbox: For Use with MATLAB , Natick : Math Works .
  • Gu , K. 1997 . Discretized LMI set in the stability problem of linear uncertain time-delay systems . International Journal Control , 68 : 923 – 934 .
  • Gu , K. 1999a . A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems . International Journal of Robust and Nonlinear Control , 9 : 1 – 14 .
  • Gu , K. Partial solution of LMI in stability problem of time-delay systems . Proceedings of the 38th IEEE Conference on Decision and Control . Madison. pp. 227 – 232 . Omnipress .
  • Gu , K. and NICULESCU , S.-I. 2000 . Additional dynamics in transformed time-delay systems . IEEE Transaction on Automatic Control , 45 : 572 – 575 .
  • HALE , J. K. and VERDUYN LUNEL , S. M. 1993 . Introduction to Functional Differential Equations , New York : Springer .
  • HAN , Q.-L. and Gu , K. 2000 . Criteria for stability of uncertain linear systems with time-varying delay . International Journal of Applied Mathematics and Computer Science , 10 : 205 – 225 .
  • HAN , Q.-L. and Gu , K. 2001a . On robust stability of time-delay systems with norm-bounded uncertainty . IEEE Transactions on Automatic Control , 46 : 1426 – 1431 .
  • HAN , Q.-L. and Gu , K. Robust stability of time-delay systems with block-diagonal uncertainty . 40th IEEE Conference on Decision and Control . February, December 4-7 2001 . Orlando, FL, USA
  • HAN , Q.-L. and MEHDI , D. Robust Hx controller synthesis for uncertain systems with multiple time-varying delays: an LMI approach . Proceedings of the 14th IFAC World Congress . Oxford. pp. 271 – 276 . Elsevier .
  • HAN , Q.-L. and MEHDI , D. 1999b . Robust stabilization for uncertain time-varying delay constrained systems with delay-dependence . International Journal of Applied Mathematics and Computer Science , 9 : 293 – 311 .
  • HUANG , W. 1989 . Generalization of Liapunov's theorem in a linear delay system . Journal of Mathematical Analysis and Applications , 142 : 83 – 94 .
  • KHARITONOV , V. L. and MELCHOR-AGUILAR , D. A. 2000 . On delay-dependent stability conditions . Systems and Control Letters , 40 : 71 – 76 .
  • KHARITONOV , V. L. and MELCHOR-AGUILAR , D. A. Additional dynamics for time varying systems with delay . 40th IEEE Conference on Decision and Control . December 4-7 2001 , Orlando, FL, USA.
  • KOKAME , H. , KOBAYASHI , H. and MORI , T. 1998 . Robust H8 performance for linear delay-differential systems with time-varying uncertainties . IEEE Transactions on Automatic Control , 43 : 223 – 226 .
  • Li , X. and DE SOUZA , C. E. 1997 . Criteria for robust stability and stabilization of uncertain linear systems with state delay . Automatica , 33 : 1657 – 1662 .
  • MALEK-ZAVAREI , M. and JAMSHIDI , M. 1987 . Time Delay Systems: Analysis. Optimization and Applications , Amsterdam : North-Holland .
  • MORI , T. 1985 . Criteria for asymptotic stability of linear time-delay systems . IEEE Transactions on Automatic Control , 30 : 158 – 161 .
  • NICULESCU , S.-I. , NETO , A. T. , DUGARD , L. and DION , J. M. Delay-dependent stability of linear systems with delayed state: an LMI approach . Proceedings of the 34th IEEE Conference on Decision and Control . Madison. pp. 1495 – 1496 . Omnipress .
  • PARK , P. 1999 . A delay-dependent stability criterion for systems with uncertain time-invariant delays . IEEE Transactions on Automatic Control , 44 : 876 – 877 .
  • PHOOIARUENCHANACHAI , S. and FURUTA , K. 1992 . Memoryless stabilization of uncertain linear systems including time-varying state delays . IEEE Transactions on Automatic Control , 37 : 1022 – 1026 .
  • REPIN , Yu. M. 1957 . On stability of solutions of equations with argument delay . Applied Mathematics and Mechanics , 21 : 253 – 261 .
  • SHEN , J. C. , CHEN , B. S. and KUNO , F. C. 1991 . Memory less stabilization of uncertain dynamic delay systems: Riccati equation approach . IEEE Transactions on Automatic Control , 36 : 638 – 640 .
  • Su , J.-H. 1994 . Further results on the robust stability of linear systems with a single delay . Systems and Control Letters , 23 : 375 – 379 .
  • Su , T. J. and HUANG , C. G. 1992 . Robust stability of delay dependence for linear uncertain systems . IEEE Transactions on Automatic Control , 37 : 1656 – 1659 .
  • Xu , B. 1994 . Comments on 'Robust stability of delay dependence for linear uncertain systems' . IEEE Transactions on Automatic Control , 39 : 2365

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.