Guaranteed Cost Observer–Based Controls for a Class of Uncertain Neutral Time-Delay Systems

  • C. H. Lien


In this paper, guaranteed-cost observer-based controls for a class of uncertain neutral time-delay systems are considered. The asymptotic stabilization for the uncertain neutral systems is guaranteed with an observer-based feedback control. The linear matrix inequality (LMI) approach is used to design the observer-based feedback control system. Two classes of observer-based controls are proposed and their guaranteed costs are given. The control and observer gains are given from the LMI feasible solutions. A convex optimization problem with LMIs is formulated to design the optimal guaranteed-cost observer-based controls which minimize the guaranteed cost of the system considered. A numerical example is given to illustrate the results.


Robust observer-based control guaranteed-cost control LMI approach neutral time-delay systems 


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  1. 1.
    Busawon, K.K., Saif, M. 1999A State Observer for Nonlinear Systems, IEEE Transactions on Automatic Control.4420982103Google Scholar
  2. 2.
    Gu, D.W., Poon, F.W. 2001A Robust State Observer SchemeIEEE Transactions on Automatic Control.4619581963CrossRefGoogle Scholar
  3. 3.
    Jo, N.H., Seo, J.H. 2002Observer Design for Nonlinear Systems That Are Not Uniformly ObservableInternational Journal of Control.75361380CrossRefGoogle Scholar
  4. 4.
    Sun, Y.J. 2002Global Stabilizability of an Uncertain System with Time-Varying Delays via Dynamics Observer-Based Output FeedbackLinear Algebra and Its Applications.35391105CrossRefGoogle Scholar
  5. 5.
    Tan, C.P., Edwards, C. 1998An LMI Approach for Designing Sliding-Mode ObserversInternational Journal of Control.7415591568Google Scholar
  6. 6.
    Zitek, P. 1999Anisochronic State Observers for Hereditary SystemsInternational Journal of Control.71581599CrossRefGoogle Scholar
  7. 7.
    Hale, J.K., Verduyn Lunel, S.M. 1993Introduction to Functional Differential EquationsSpringer VerlagNew York, NYGoogle Scholar
  8. 8.
    Kolmanoskii, V.B., Myshkis, A. 1992Applied Theory of Functional Differential EquationsKluwer Academic PublishersDordrecht, NetherlandsGoogle Scholar
  9. 9.
    Nian, X., Feng, J. 2003Guaranteed-Cost Control of a Linear Uncertain System with Multiple Time-Varying Delays: An LMI ApproachIEE Proceedings on Control Theorey and Applications.1501722CrossRefGoogle Scholar
  10. 10.
    Park, J.H. 2003Robust Guaranteed Cost Control for Uncertain Linear Differential Systems of Neutral TypeApplied Mathematics and Computation.140523535CrossRefGoogle Scholar
  11. 11.
    Park, J.H. 2003Guaranteed Cost Stabilization of Neutral Differential Systems with Parametric UncertaintyJournal of Computation and Applied Mathematics.151317382Google Scholar
  12. 12.
    Xu, S., Lam, J., Yang, C., Verrist E, I. 2003An LMI Approach to Guaranteed Cost Control for Uncertain Linear Neutral Delay SystemsInternational Journal of Robust Nonlinear Control.133553CrossRefGoogle Scholar
  13. 13.
    Yu, L., Chu, J. 1999An LMI Approach to Guaranteed Cost Control of Linear Uncertain Time-Delay SystemsAutomatica.3511551159CrossRefMathSciNetGoogle Scholar
  14. 14.
    Crusius, C.A.R., Trofino, A. 1999Sufficient LMI Conditions for Output Feedback Control ProblemsIEEE Transactions on Automatic Control.4410531057CrossRefGoogle Scholar
  15. 15.
    Kuo C.H., Fang C.H. (2003). Stabilization of Uncertain Linear Systems via Static Output Feedback Control. 2003 Automatic Control Conference. Taipei, Taiwan, Vol. 1, pp 1607–1611Google Scholar
  16. 16.
    Lu, C.Y., Tsai, J.S.H., Jong, G.J., Su, T.J. 2003An LMI-Based Approach for Robust Stabilization of Uncertain Stochastic Systems with Time-Varying DelaysIEEE Transactions on Automatic Control.48286289CrossRefGoogle Scholar
  17. 17.
    Lien, C.H., Chen, J.D. 2003Discrete Delay-Independent and Discrete Delay Dependent Criteria for a Class of Neutral Systems, ASME Journal of Dynamics SystemsMeasurement, and Control.1253341Google Scholar
  18. 18.
    Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V. 1994Linear Matrix Inequalities in System and Control TheorySIAMPhiladelphia, PennsylvaniaGoogle Scholar
  19. 19.
    Zhou, K., Doyle, J.C. 1998Essentials of Robust ContolPrentice HallUpper Saddle River, New JerseyGoogle Scholar
  20. 20.
    Callier, F.M., Desoer, C.A. 1991Linear System TheorySpringer VerlagNew York, NYGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • C. H. Lien
    • 1
  1. 1.Department of Electrical EngineeringI-Shou UniversityKaohsiungROC

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