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On stabilizing uncertain linear delay systems

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Abstract

This note concerns the stabilization problem for linear delay systems containing uncertain elements. If the so-called matching conditions are satisfied and the uncertainties in the control matrix are not too large, there exist linear current-response feedback controls which guarantee asymptotic stability of the zero response of the system, no matter what the uncertainties and initial conditions are.

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References

  1. Kwon, W. H., andPearson, A. E.,A Note on Feedback Stabilization of a Differential-Difference System, IEEE Transactions on Automatic Control, Vol. AC-22, No. 3, 1977.

  2. Feliachi, A., andThowsen, A.,Memoryless Stabilization of Linear Delay-Differential Systems, IEEE Transactions on Automatic Control, Vol. 26, No. 2, 1981.

  3. Lee, T. N., andDianat, S.,Stability of Time-Delay Systems, IEEE Transactions on Automatic Control, Vol. 26, No. 4, 1981.

  4. Leitmann, G.,Guaranteed Ultimate Boundedness for a Class of Uncertain Linear Dynamical Systems, IEEE Transactions on Automatic Control, Vol. AC-23, No. 6, 1978.

  5. Leitmann, G.,Guaranteed Asymptotic Stability for Some Linear Systems with Bounded Uncertainties, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 101, No. 3, 1979.

  6. Leitmann, G.,On the Efficacy of Nonlinear Control in Uncertain Linear Systems, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 103, No. 2, 1981.

  7. Corless, M., andLeitmann, G.,Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems, IEEE Transactions on Automatic Control, Vol. 26, No. 6, 1981.

  8. Barmish, B. R., Corless, M., andLeitmann, G.,A New Class of Stabilizing Controllers for Uncertain Dynamic Systems, SIAM Journal on Control and Optimization (to appear).

  9. Hale, J.,Theory of Functional Differential Equations, Springer-Verlag, New York, New York, 1977.

    Google Scholar 

  10. Kreindler, E., andJameson, A.,Conditions for Nonnegativeness of Partitioned Matrices, IEEE Transactions on Automatic Control, Vol. 17, No. 1, 1972.

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Authors and Affiliations

  1. Department of Applied Mathematics, Huazhong University of Science and Technology, Wuhan, Peoples Republic of China

    Y. Yu (Associate Professor)

Authors
  1. Y. Yu
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Additional information

Communicated by G. Leitmann

This paper is based, in part, on research supported by NSF under Grant No. ECS-82-10324.

The author would like to thank Professor G. Leitmann and Mr. M. Corless for their comments, which have led to an improvement in both the quality and clarity of this note.

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Yu, Y. On stabilizing uncertain linear delay systems. J Optim Theory Appl 41, 503–508 (1983). https://doi.org/10.1007/BF00935369

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  • DOI: https://doi.org/10.1007/BF00935369

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