Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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A study on stability bounds of time-varying perturbations

시변 섭동의 안정범위에 관한 연구

  • Kim, Byung-Soo (Automatic Control Research Center, Dept.of Electirc Engineering, Seoul National University) ;
  • Han, Hyung-Seok (Soonchungyang University) ;
  • Lee, Jang-Gyu (Automatic Control Research Center, Dept.of Electirc Engineering, Seoul National University)
  • 김병수 (서울대학교 전기공학부, 자동제어특화연구센터) ;
  • 한형석 (순천향대학교 전기전자공학부) ;
  • 이장규 (서울대학교 전기공학부, 자동제어특화연구센터)
  • Published : 1997.02.01
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Abstract

The stability robustness problem of linear discrete-time systems with time-varying perturbations is considered. By using Lyapunov direct method, the perturbation bounds for guaranteeing the quadratic stability of the uncertain systems are derived. In the previous results, the perturbation bounds are derived by the quadratic equation stemmed from Lyapunov method. In this paper, the bounds are obtained by a numerical optimization technique. Linear matrix inequalities are proposed to compute the perturbation bounds. It is demonstrated that the suggested bound is less conservative for the uncertain systems with unstructured perturbations and seems to be maximal in many examples. Furthermore, the suggested bound is shown to be maximal for the special classes of structured perturbations.

Keywords

References

  1. International Journal of Control v.50 no.1 Stability robustness of linear discrete-time systems in the presence of uncertainty E. Yaz;X. Niu
  2. International Journal of Control v.50 no.1 Robust stability bounds on time-varying perturbations for state-space models of linear discrete-time systems S. R. Kolla;R. K. Yedavalli;J. B. Farison
  3. International Journal of Control v.48 no.5 Robust stability of discrete systems M. E. Sezer;D. D. Siljak
  4. IEEE Transactions on Automatic Control v.36 no.7 Robustness of discrete-time systems for unstructured stochastic perturbations E. Yaz;X. Niu
  5. Internaitonal Journal of Control v.60 no.2 Stability robustness bound estimates of discrete systems : analysis and comparison M. Halicka;D. Rosinova
  6. Nonlinear programming theory and algorithms(2nd edition) M. S. Bazaraa;H. D. Sherali;C. M. Shetty
  7. Linear controller design-limits of performance S. P. Boyd;C. H. barratt
  8. Linear matrix inequalities in system and control theory S. P. Boyd;L. E. Ghaoui;E. Feron;V. Balakrishnan
  9. International Journal of Control v.46 no.5 Stability robustness analysis of digital control systems in state-space models Y. Juang;T. Kuo;C. Hsu
  10. IEEE Transactions on Automatic Control v.36 no.6 A necessary and sufficient condition for the stability fo nonnegative interval discrete systems B. Shafai;K. Perev;D. Cowley;Y. Chehab
  11. Automatica v.26 no.3 Computer-aided determination of stability robustness measure of linear discrete-time systems M. Eslami
  12. IEEE Transactions on Automatic Control v.38 no.2 Explicit asymmetric bounds for robust stability of continuous and discrete-time systems Z. Gao;P. J. Antsakiis
  13. International Journal of Control v.59 no.4 Necessary and sufficient conditions for stability of time-varying discrete interval matrices H. S. Han;J. G. Lee
  14. International Journal fo Control v.61 no.6 Lyapunov stability robust analysis and robustness design for linear continuous-time systems J. S. Luo;A. Johnson;P. P. Van Den Bosch
  15. IEEE Transactions on Automatic Control v.39 no.1 Designing stabilizing control of uncertain systems by quasiconvex optimization K. Gu
  16. Matrix Analysis R. A. Horn;C. R. Johnson
  17. Linear systems T. Kailath