Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2003.9.8.616

Estimation of the Asymptotic Stability Region for the Uncertain Variable Structure Systems with Bounded Controllers  

최한호 (동국대학교 전기공학과)
국태용 (성균관대학교 전기공학과)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.9, no.8, 2003 , pp. 616-622 More about this Journal
Abstract
This paper deals with the problem of estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded controllers. Using linear matrix inequalities(LMIs) we estimate the ASR and show the exponential stability of the closed-loop control system in the estimated ASR. We give a simple LMI-based algorithm to get estimates of the ASR. We also give a synthesis algorithm to design a switching surface which will make the estimated ASR big. Finally, we give numerical examples in order to show that our method can give better results than the previous ones for a certain class of uncertain variable structure systems with bounded controllers.
Keywords
linear matrix inequality(LMI); variable structure system; bounded control; switching surface; asymptotic stability region;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 S. M. Madani-Esfahani, M. Hached and S. H. Zak, 'Estimation of sliding mode domains of uncertain variable structure systems with bounded controllers,' IEEE Trans. Automat. Contr., vol. 35, pp. 446-449, 1990   DOI   ScienceOn
2 H. H. Choi and M. J. Chung, 'Estimation of asymptotic stability region of uncertain systems with bounded sliding mode controllers,' IEEE Trans. Automat. Contr., vol. 39, pp. 2275-2278, 1994   DOI   ScienceOn
3 P. Gahinet and P. Apkarian, 'A linear matrix inequality approach to $H_{\infty}$ control,' Int. J. Robust and Nonlinear Control., vol. 4, pp. 421-448, 1994   DOI
4 P. Gahinet, A. Nemirovski and A. J. Laub, LMI Control Toolbox User's Guide, Natic, MA:The Math Works Inc., 1995
5 V. I. Utkin, 'Variable structure systems with sliding modes,' IEEE Trans. Automat. Contr., vol. 22, pp. 212-222, 1977   DOI
6 H. H. Choi, 'On the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties,' Automatica, vol. 35, pp. 1707-1715, 1999   DOI   ScienceOn
7 A. Albert, 'Conditions for positive and nonnegative definiteness in terms of pseudoinverses,' SIAM J. Appl. Math., vol. 17, pp. 434-440, 1969   DOI   ScienceOn