NEW STABILITY CRITERIA FOR INTERVAL TIME-DELAY SYSTEMS BY IMPROVED INTEGRAL INEQUALITIES

Yan Bai, Zhichen Li, Congzhi Huang, and Huaicheng Yan

References

  1. [1] B. Chebbi, D. Lazaroff, and P.X. Liu, A collaborative virtualhaptic environment for surgical training and tele-mentoring,International Journal of Robotics & Automation, 22(1), 2007,69–78.
  2. [2] Y. Shen, W. Shen, and J. Gu, Sliding-mode control for tele-robotic neurosurgical system, International Journal of Robotics& Automation, 22(1), 2007, 19–31.
  3. [3] J.H. Kim, Note on stability of linear systems with time-varyingdelay, Automatica, 47(9), 2011, 2118–2121.
  4. [4] S. Thomas and S.J. Mija, A practically implementable dis-crete time sliding mode controller for flexible manipulator,International Journal of Robotics & Automation, 23(4), 2008,235–241.
  5. [5] H.C. Yan, F.F. Qian, H. Zhang, F.W. Yang, and G. Guo, H∞fault detection filtering for mechanical spring-mass systemsover networked systems with incomplete information, IEEETransactions on Industrial Electronics, 63(9), 2016, 5622–5631.
  6. [6] W.II. Lee and P.G. Park, Second-order reciprocally convexapproach to stability of systems with interval time-varyingdelays, Applied Mathematics and Computation, 229, 2014,245–253.
  7. [7] H.J Liu and K.Y. Young, Applying wave-variable-based slidingmode impedance control for robot teleoperation, InternationalJournal of Robotics & Automation, 26(3), 2011, 296–304.
  8. [8] P.L. Liu, Further improvement on delay-range-dependent sta-bility results for linear systems with interval time-varyingdelays, ISA Transactions, 52(6), 2013, 725–729.
  9. [9] L.Y. Hu, Y.B. Yang, and S.P. Xu, Force feedback and con-trol for wave-variable teleoperation systems with time delays,International Journal of Robotics & Automation, 29(4), 2014,338–348.
  10. [10] H.C. Yan, F.F. Qian, F.W. Yang, and H.B. Shi, H∞ filteringfor nonlinear networked systems with randomly occurring dis-tributed delays, missing measurements and sensor saturation,Information Sciences, 370–371, 2016, 772–782.
  11. [11] M. Tang, Y.W. Wang, and C. Wen, Improved delay-range-dependent stability criteria for linear systems with intervaltime-varying delays, IET Control Theory & Applications, 6(6),2012, 868–873.
  12. [12] X.L. Zhu, Y. Wang, and G.H. Yang, New stability criteria forcontinuous-time systems with interval time-varying delay, IETControl Theory & Applications, 4(6), 2010, 1101–1107.
  13. [13] W. Qian, T. Li, S. Cong, and S. Fei, Stability analysis forinterval time-varying delay systems based on time-varyingbound integral method, Journal of the Franklin Institute,351(10), 2014, 4892–4903.
  14. [14] P.G. Park, J.W. Ko, and C. Jeong, Reciprocally convexapproach to stability of systems with time-varying delays,Automatica, 47(1), 2011, 235–238.
  15. [15] J. Sun, G.P. Liu, J. Chen, and D. Rees, Improved delay-range-dependent stability criteria for linear systems with time-varyingdelays, Automatica, 46(2), 2010, 466–470.
  16. [16] J.J Hui, X.Y. Kong, H.X. Zhang, and X. Zhu, Delay-partitioning approach for systems with interval time-varyingdelay and nonlinear perturbations, Journal of Computationaland Applied Mathematics, 281, 2015, 74–81.
  17. [17] A. Farnam and R.M. Esfanjani, Improved linear matrix in-equality approach to stability analysis of linear systems withinterval time-varying delays, Journal of Computational andApplied Mathematics, 294, 2016, 49–56.
  18. [18] C. Wang and Y. Shen, Delay partitioning approach to robuststability analysis for uncertain stochastic systems with intervaltime-varying delay, IET Control Theory & Applications, 6(7),2012, 875–883.
  19. [19] J. An, Z. Li, and X. Wang, A novel approach to delay-fractional-dependent stability criterion for linear systems withinterval delay, ISA Transactions, 53(2), 2014, 210–219.
  20. [20] A. Seuret and F. Gouaisbaut, Wirtinger-based integral inequal-ity: Application to time-delay systems, Automatica, 49(9),2013, 2860–2866.
  21. [21] M.J. Park, O.M. Kwon, J.H. Park, S.M. Lee, E.J. Cha, etal., Stability of time-delay systems via Wirtinger-based doubleintegral inequality, Automatica, 55, 2015, 204–208.
  22. [22] L.V. Hien and H. Trinh, An enhanced stability criterion fortime-delay systems via a new bounding technique, Journal ofthe Franklin Institute, 352(10), 2015, 4407–4422.
  23. [23] L.V. Hien and H. Trinh, Refined Jensen-based inequalityapproach to stability analysis of time-delay systems, IETControl Theory & Applications, 9(14), 2015, 2188–2194.
  24. [24] P. Park, W.II. Lee, and S.K. Lee, Auxiliary function-basedintegral inequalities for quadratic functions and their applica-tions to time-delay systems, Journal of the Franklin Institute,352(4), 2015, 1378–1396.
  25. [25] P.L. Liu, Improved delay-range-dependent robust stabilityfor uncertain systems with interval time-varying delay, ISATransactions, 53(6), 2014, 1731–1738.
  26. [26] Y. Liu, L.S. Hu, and P. Shi, A novel approach on stabilizationfor linear systems with time-varying input delay, AppliedMathematics and Computation, 218(10), 2012, 5937–5947.
  27. [27] O.M. Kwon, M.J. Park, J.H. Park, S.M. Lee, E.J. Cha, etal., Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality, Journalof the Franklin Institute, 351(12), 2014, 5386–5398.
  28. [28] H.J. Gao, T.W. Chen, and J. Lam, A new delay systemapproach to network-based control, Automatica, 44(1), 2008,39–52.

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