Skip to main content
SpringerLink
Log in

Delay-independent stabilization of uncertain linear systems of neutral type

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, we show that a sufficient condition for the delay-independent stabilizability of linear delay systems, which had been obtained by Amemiya et al., is also valid for linear neutral systems with measurable state variables by a new differential-difference inequality.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barmish, B. R., andLeitmann, G.,On Ultimate Boundedness Control of Uncertain Systems in the Absence of Matching Assumptions, IEEE Transactions on Automatic Control, Vol. 27, pp. 153–158, 1982.

    Article  Google Scholar 

  2. Barmish, B. R., Corless, M., andLeitmann, G.,A New Class of Stabilizing Controllers for Uncertain Dynamical Systems, SIAM Journal on Control and Optimization, Vol. 21, pp. 246–255, 1983.

    Article  Google Scholar 

  3. Barmish, B. R.,Stabilization of Uncertain Systems via Linear Control, IEEE Transactions on Automatic Control, Vol. 28, pp. 848–850, 1983.

    Article  Google Scholar 

  4. Barmish, B. R.,Necessary and Sufficient Conditions for Quadratic Stabilizability of an Uncertain System, Journal of Optimization Theory and Applications, Vol. 46, pp. 399–408, 1985.

    Article  Google Scholar 

  5. Gutman, S., andPalmor, Z.,Properties of Min-Max Controllers in Uncertain Dynamical Systems, SIAM Journal on Control and Optimization, Vol. 20, pp. 850–861, 1983.

    Article  Google Scholar 

  6. Leitmann, G.,Guaranteed Asymptotic Stability for Some Linear Systems with Bounded Uncertainties, Journal of Dynamical Systems, Measurement, and Control, Vol. 101, pp. 212–216, 1979.

    Google Scholar 

  7. Leitmann, G.,On the Efficacy of Nonlinear Control in Uncertain Linear Systems, Journal of Dynamical Systems, Measurement, and Control, Vol. 102, pp. 94–102, 1981.

    Google Scholar 

  8. Wei, K. H.,Quadratic Stabilizability of Linear Systems with Structural Independent Time-Varying Uncertainties, IEEE Transcactions on Automatic Control, Vol. 35, pp. 268–277, 1990.

    Article  Google Scholar 

  9. Akazawa, K., Amemiya, T., andTokumaru, H.,Further Condition for the Delay-Independent Stabilization of Linear Systems, International Journal of Control, Vol. 46, pp. 1195–1202, 1987.

    MathSciNet  Google Scholar 

  10. Amemiya, T.,Delay-Independent Stabilization of Linear Systems, International Journal of Control, Vol. 37, pp. 1071–1079, 1983.

    Google Scholar 

  11. Amemiya, T., Akazawa, K., andTokumaru, H.,Delay-Independent Stabilization and Decay Rate Assignability of Linear Systems with Limited Measurable State Variables, International Journal of Control, Vol. 47, pp. 65–73, 1988.

    Google Scholar 

  12. Amemiya, T., andLeitmann, G.,A Method for Designing a Stabilizing Control for a Class of Uncertain Linear Delay Systems, Dynamics and Control, Vol. 4, pp. 147–167, 1994.

    Article  Google Scholar 

  13. Thowsen, A.,Uniform Ultimate Boundedness of the Solutions of Uncertain Dynamic Delay Systems with State-Dependent and Memoryless Feedback Control, International Journal of Control, Vol. 37, pp. 1135–1143, 1983.

    Google Scholar 

  14. Tokumaru, H., Adachi, N., andAmemiya, T.,Macroscopic Stability of Interconnected Systems, Paper 44-4, Proceeding of the 6th IFAC World Congress, Boston, Massachusetts, 1975.

  15. Ma, W. B.,On the Exponential Stability of Linear Difference Systems with Time-Varying Lags, Chinese Journal of Contemporary Mathematics, Vol. 9, pp. 185–191, 1988.

    Google Scholar 

  16. Ma, W. B.,The Stability of Large-Scale Dynamical Systems with Delays by Vector VFunctions, Acta Mathematicae Applicate Sinica, Vol. 12, pp. 24–29, 1989 (in Chinese).

    Google Scholar 

  17. Chukwu, E. N.,Stability and Time-Optimal Control of Hereditary Systems, Academic Press, New York, New York, 1992.

    Google Scholar 

  18. Connor, D. A. O., andTarn, T. J.,On the Function Space Controllability of Linear Neutral Systems, SIAM Journal on Control and Optimization, Vol. 21, pp. 306–329, 1983.

    Article  Google Scholar 

  19. Connor, D. A. O., andTarn, T. J.,On Stabilization by State Feedback for Neutral Differential Difference Equations, IEEE Transactions on Automatic Control, Vol. 28, pp. 615–618, 1983.

    Article  Google Scholar 

  20. Jacobs, M. Q., andLangenhop, C. E.,Criteria for the Function-Space Controllability of Linear Neutral Systems, SIAM Journal on Control and Optimization, Vol. 14, pp. 1009–1048, 1976.

    Article  Google Scholar 

  21. Kolmanovskii, V. B., andNosov, V. R.,Stability of Functional Differential Equations, Academic Press, New York, New York, 1986.

    Google Scholar 

  22. Berman, A., andPlemmons, R. J.,Nonnegative Matrices in the Mathematical Science, Academic Press, New York, New York, 1979.

    Google Scholar 

  23. Si, L. G., andMa, W. B.,Differential-Difference Inequalities with Unbounded Delays and Their Applications, Journal of Nonlinear Analysis: Theory, Methods, and Applications, Vol. 17, pp. 787–801, 1991.

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Author notes

  1. W. B. Ma (Associate Professor)

    Present address: Department of Applied Systems Science, Faculty of Engineering, Kyoto University, Kyoto, Japan

Authors and Affiliations

  1. Department of Mathematics, Inner Mongolia Normal University, Huhhot, P. R. China

    W. B. Ma (Associate Professor)

  2. Department of Applied Systems Science, Faculty of Engineering, Kyoto University, Kyoto, Japan

    N. Adachi (Professor)

  3. Tokyo Metropolitan Institute of Technology, Tokyo, Japan

    T. Amemiya (Professor)

Authors
  1. W. B. Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Adachi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Amemiya
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

The authors express their appreciation to Professor G. Leitmann for his useful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ma, W.B., Adachi, N. & Amemiya, T. Delay-independent stabilization of uncertain linear systems of neutral type. J Optim Theory Appl 84, 393–405 (1995). https://doi.org/10.1007/BF02192121

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02192121

Key words

Search

Navigation