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On the robustness of linear stabilizing feedback control for linear uncertain systems

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Abstract

We investigate linear time-invariant scalar-input systems with constant uncertainties that are not required to satisfy matching conditions. In a previous paper, the existence of stabilizing discontinuous controllers is established under three assumptions for such systems. The first assumption requires controllability of the system for each uncertainty. The second is a condition on an uncertain Lyapunov equation, and the third is a boundedness condition related to the controllability matrix. In this paper, using the same assumptions, we show the existence of a linear stabilizing control. Our result is related to the high-gain theorem of classical control.

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References

  1. Barmish, B. R., Petersen, I. R., andFeuer, A.,Linear Ultimate Boundedness Control of Uncertain Dynamical Systems, Automatica, Vol. 19, No. 5, pp. 523–532, 1983.

    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, No. 2, pp. 246–255, 1983.

    Google Scholar 

  3. Stalford, H.,Robust Control of Uncertain Systems in the Absence of Matching Conditions: Scalar Input, Proceedings of the IEEE Conference on Decision and Control, Los Angeles, California, 1987.

  4. Kailath, T.,Linear Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1980.

    Google Scholar 

  5. Stalford, H., andChao, C. H.,A Necessary and Sufficient Condition in Lyapunov Robust Control, Journal of Optimization Theory and Applications, Vol. 63, No. 2, pp. 191–204, 1989.

    Google Scholar 

  6. Stalford, H., andGarrett, F., Jr.,Robust Nonlinear Control for High Angle-of-Attack Flight, Paper No. AIAA-87-0346, AIAA 25th Aerospace Sciences Meeting, Reno, Nevada, 1987.

  7. Stalford, H.,Target Tracking at High α Using Certain Robust Nonlinear Controllers, Paper No. AIAA-87-2407, AIAA Guidance, Navigation, and Control Conference, Monterey, California, 1987.

  8. Stalford, H.,On Robust Control of Wing Rock Using Nonlinear Control, American Control Conference, Minneapolis, Minnesota, pp. 1890–1899, 1987.

  9. Leitmann, G.,Guaranteed Asymptotic Stability for Some Linear Systems with Bounded Uncertainties, Journal of Dynamic Systems, Measurement, and Control, Vol. 101, No. 3, pp. 212–216, 1979.

    Google Scholar 

  10. Leitmann, G.,On the Efficacy of Nonlinear Control in Uncertain Linear Systems, Journal of Dynamic Systems, Measurement, and Control, Vol. 102, No. 2, pp. 95–102, 1981.

    Google Scholar 

  11. Davison, E. J., andWang, S. H.,Properties and Calculations of Transmission Zeros of Linear Multivariate Systems, Control System Design by Pole-Zero Assignment, Edited by F. Fallside, Academic Press, New York, New York, pp. 16–42, 1977.

    Google Scholar 

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Author notes

  1. H. L. Stalford (Associate Professor)

    Present address: School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia

  2. C. H. Chao (Graduate Student)

    Present address: Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China

Authors and Affiliations

  1. Interdisciplinary Center of Applied Mathematics and Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    H. L. Stalford (Associate Professor)

  2. Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    C. H. Chao (Graduate Student)

Authors
  1. H. L. Stalford
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  2. C. H. Chao
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Communicated by G. Leitmann

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Stalford, H.L., Chao, C.H. On the robustness of linear stabilizing feedback control for linear uncertain systems. J Optim Theory Appl 63, 205–212 (1989). https://doi.org/10.1007/BF00939574

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