Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
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Improvement of the Robustness Bounds of the Linear Systems with Structured Uncertainties

구조화된 불확실성의 비선형요소를 갖는 선형 시스템의 강인영역 개선

  • Jo, Jang-Hyen (Dept. of Mechanical Engineering, Halla University)
  • 조장현 (한라대학교 기계공학부)
  • Published : 2001.01.01
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Abstract

The purpose of this paper is the derivation and development of the new definitions and methods for the new estimation of robustness for the systems having structured uncertainties. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. The systems considered are assumed to be nominally linear, with time-variant, nonlinear bounded perturbations. This new techniques demonstrate the improvement of robustness bounds from the numerical results.

Keywords

References

  1. Vannelli, A., and Vidyasagar, M., 'Maximal Lyapunov function and domains of attraction for autonomous nonlinear systems,' Automatica, Vol. 21, No. 1, pp. 69-80, 1985 https://doi.org/10.1016/0005-1098(85)90099-8
  2. Patel, R. V., and Toda, M., 'Quantitative measures of robustness for multivariable systems,' in Proceedings of Joint Automatic Control Conference, San Francisco, CA, TP8-A., 1980
  3. Patel, R. V., Toda, M. and Sridhar R., 'Robustness of linear quadratic state feedback disigns in the presence of system uncertainty,' IEEE Transactions on Automatic Control, Vol. AC-22, pp. 945-947, Dec. 1977
  4. Yeadavlli, R.K., and Liang, Z., 'Reduced conservatism in stability robustness bounds by state transformation,' IEEE Transactions on Automatic Control, Vol. AC-31, No. 9, pp. 863-866, Sep. 1986
  5. Yeadavalli, R.K., 'Perturbation bounds for robust stability in linear state space models,' International Journal of Control, Vol. 42, pp. 1507-1517, Dec. 1985 https://doi.org/10.1080/00207178508933441
  6. Yeadavalli, R.K., 'Improved measures of stability robustness for linear state space models,' IEEE Transactions on Automatic Control, Vol. AC-30, Jun. 1985, pp. 577-579
  7. Brayton, R.K., and Tong, C.H., 'Constructive Stability and asymptotic stability of dynamic systems,' IEEE Transactions on Circuits and Systems, Vol. 27, pp. 1121-1130, 1980
  8. Biernacki, R.M., Hwang, H., and Bhattacharyya, S.P., 'Robust Stability with structured parameter pertubations,' IEEE Transations on Automatic Control, Vol. AC-32, pp. 495-506, 1987
  9. Desoer, C.A., and Chan, W.S., 'Robustness of Stability conditions for linear time-variant feedback systems,' IEEE Transactions on Automatic Control, Vol. AC-22, pp. 586-590, Aug. 1977
  10. Zhou, K., and Khargonekar, P.P., 'Stability robustness bounds for linear state-space models with structured uncertainty,' IEEE Transactions on Automatic Control, Vol. AC-32, pp. 621-623, 1987
  11. Siljak, D.D., 'Parameter space methods for robust control design: A guide tour,' IEEE Transactions on Automatic Control, Vol. 34, No. 7, pp. 674-688, Jul. 1989 https://doi.org/10.1109/9.29394
  12. Singh, S. N., and Coelho, Antonio A. R., 'Nonlinear control of mismatched uncertain linear systems and application to control of aircraft,' Journal of Dynamic Systems, Measurement, and Control, Vol. 106, pp. 106-210, Sep. 1984
  13. Sundararajan, N., 'Sensitivity reduction in aircraft control systems,' IEEE Transaction on Aerospace Electrical Systems, Vol. 14, pp. 292-297, Mar. 1978 https://doi.org/10.1109/TAES.1978.308650