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An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays

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Abstract

In this paper, the problem of stability analysis for uncertain dynamic systems with time-varying delays is considered. The parametric uncertainties are assumed to be bounded in magnitude. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities, which can be solved easily by various efficient convex optimization algorithms. Two numerical examples are illustrated to show the effectiveness of proposed method.

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References

  1. Udwadia, F.E., Weber, H.I., Leitmann, G.: Dynamical Systems and Control. Chapman & Hall/CRC, London (2004)

    MATH  Google Scholar 

  2. Leitmann, G., Udwadia, F.E., Kryazhimskii, A.V.: Dynamics and Control. CRC Press, Boca Raton (1999)

    MATH  Google Scholar 

  3. Hale, J., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)

    MATH  Google Scholar 

  4. Kolmanovskii, V.B., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic, Boston (1992)

    Google Scholar 

  5. Phohomsiri, P., Udwadia, F.E., Von Bremmen, H.: Time-delayed positive velocity feedback control design for active control of structures. J. Eng. Mech. 132, 690–703 (2006)

    Article  Google Scholar 

  6. Udwadia, F.E., Hosseini, M.A.M., Chen, Y.H.: Robust control of uncertain systems with time varying delays in control input. In: Proceedings of the American Control Conference, Albuquerque, New Mexico, pp. 3641–3644 (1997)

  7. Park, J.H., Won, S.: A note on stability of neutral delay-differential systems. J. Franklin Inst. 336, 543–548 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Park, J.H., Won, S.: Asymptotic stability of neutral systems with multiple delays. J. Optim. Theory Appl. 103, 183–200 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Nam, P.T., Phat, V.N.: Robust stabilization of linear systems with delayed state and control. J. Optim. Theory Appl. 140, 287–200 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Park, J.H.: Robust stabilization for dynamic systems with multiple time-varying delays and nonlinear uncertainties. J. Optim. Theory Appl. 108, 155–174 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chen, J.D.: Delay-dependent nonfragile H ∞ observer-based control for neutral systems with time delays in the state and control input. J. Optim. Theory Appl. 141, 445–460 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kwon, O.M., Park, J.H.: On improved delay-dependent robust control for uncertain time-delay systems. IEEE Trans. Automat. Control 49, 1991–1995 (2004)

    Article  MathSciNet  Google Scholar 

  13. Kwon, O.M., Park, J.H.: Matrix inequality approach to novel stability criterion for time delay systems with nonlinear uncertainties. J. Optim. Theory Appl. 126, 643–656 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lien, C.H.: Guaranteed cost observer-based controls for a class of uncertain neutral time-delay systems. J. Optim. Theory Appl. 126, 137–156 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kwon, O.M., Park, J.H., Lee, S.M.: On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays. Appl. Math. Comput. 197, 864–873 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Lien, C.H.: Delay-dependent stability criteria for uncertain neutral systems with multiple time-varying delays via LMI approach. IEE Proc., Control Theory Appl. 152, 707–714 (2005)

    Article  Google Scholar 

  17. Niculescu, S.I.: Delay Effects on Stability: A Robust Control Approach. LNCIS, vol. 269. Springer, Berlin (2001)

    MATH  Google Scholar 

  18. Park, P.G.: A delay-dependent stability criterion for systems with uncertain linear state-delayed systems. IEEE Trans. Automat. Control 35, 876–877 (1999)

    Article  Google Scholar 

  19. Yue, D., Won, S., Kwon, O.: Delay dependent stability of neutral systems with time delay: an LMI approach. IEE Proc., Control Theory Appl. 150, 23–27 (2003)

    Article  Google Scholar 

  20. Park, J.H., Kwon, O.: On new stability criterion for delay-differential systems of neutral type. Appl. Math. Comput. 162, 627–637 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Park, P.G., Ko, J.W.: Stability and robust stability for systems with a time-varying delay. Automatica 43, 1855–1858 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  22. Gouaisbaut, F., Peaucelle, D.: Delay-dependent stability of time delay systems. In: 5th IFAC Symposium on Robust Control Design, Center of Toulouse, France (2006)

  23. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering, Chungbuk National University, Cheongju, Republic of Korea

    O. M. Kwon

  2. Department of Electrical Engineering, Yeungnam University, Kyongsan, Republic of Korea

    J. H. Park

  3. School of Electronics Engineering, Daegu University, Kyongsan, Republic of Korea

    S. M. Lee

Authors
  1. O. M. Kwon
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  2. J. H. Park
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  3. S. M. Lee
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Corresponding author

Correspondence to J. H. Park.

Additional information

Communicated by F.E. Udwadia.

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Kwon, O.M., Park, J.H. & Lee, S.M. An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays. J Optim Theory Appl 145, 343–353 (2010). https://doi.org/10.1007/s10957-009-9637-x

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  • DOI: https://doi.org/10.1007/s10957-009-9637-x

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