Delay-dependent robust stabilisation of discrete-time systems with time-varying delay

Delay-dependent robust stabilisation of discrete-time systems with time-varying delay

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The stability of discrete systems with time-varying delay is considered. New delay-dependent stability criteria are devised, which are dependent on the minimum and maximum delay bounds. An initial analysis leads to a criterion depending on an inequality involving certain matrices that can be freely chosen. By carefully choosing them to reflect the appropriate relationship between states at differing times, a stricter criterion is thereby obtained. Furthermore, new results for delay-dependent robust stabilisation of uncertain systems with time-varying delay are provided on the basis of a linear matrix inequality (LMI) framework. As the conditions obtained for the existence of admissible controllers are not expressed using strict LMI conditions, a cone complementary linearisation procedure is used to find suitable controllers. Finally, the results obtained, including the stability analysis, static output-feedback stabilisation and dynamic output feedback stabilisation are further extended to discrete time-delay systems having uncertain but norm-bounded parameters. Numerical examples demonstrate the validity of the approach proposed.


    1. 1)
    2. 2)
    3. 3)
    4. 4)
      • H.J. Gao , C.H. Wang . Robust L2–L∞ filtering for uncertain systems with multiple time-varying state delays. IEEE Trans. Circuits Syst. , 4 , 594 - 599
    5. 5)
    6. 6)
    7. 7)
    8. 8)
    9. 9)
      • Niculescu, S.I., Neto, A.T., Dion, J.M., Dugard, L.: `Delay-dependent stability of linear system with delayed state: an LMI approach', Proc. 34th IEEE Conf. on Decision Control, 1995, p. 1495–1497.
    10. 10)
    11. 11)
    12. 12)
      • X. Li , C.E. de Souza . Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach. IEEE Trans. Autom. Control , 8 , 1144 - 1148
    13. 13)
    14. 14)
    15. 15)
    16. 16)
      • L. Xie . Output feedback H∞ control of system with parameter uncertainty. Int. J. Control , 4 , 741 - 750
    17. 17)
    18. 18)

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