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


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.


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