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http://dx.doi.org/10.5302/J.ICROS.2003.9.11.861

A Linear Sliding Surface Design Method for a Class of Uncertain Systems with Mismatched Uncertainties  

최한호 (동국대학교 전기공학과)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.9, no.11, 2003 , pp. 861-867 More about this Journal
Abstract
We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.
Keywords
linear matrix inequality(LMI); variable structure system; sliding surface; uncertain system; matching condition;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 P. Gahinet, A. Nemirovski and A. J. Laub, LMI Control Toolbox User's Guide, The MathWorks Inc., 1995
2 S. Boyd, L. ElGhaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994
3 P. Lancaster and M. Tismenetsky, The Theory of Mat rices, 2nd, Academic Press, 1985
4 O. M. E. ElGhezawi, A. S. I. Zinober, and S. A. Billings, 'Analysis and design of variable structure systems using a geometric approach,' Int. J. Contr., vol. 38, pp. 657-671, 1981   DOI   ScienceOn
5 V. I. Utkin, 'Variable structure systems with sliding modes.' IEEE Trans. Automat. Contr., vol. AC-22, pp. 212-222, 1977   DOI
6 R. A. Decarlo, S. H. Zak, and G. P. Mathews, 'Variable structure control of nonlinear multi variable systems : A tutorial,' IEEE Proceedings, vol. 76, pp. 212-232, 1988   DOI   ScienceOn
7 R. H. C. Takahashi and P. L. D. Peres, ' $H_2$ guaranteed cost-switching surface design for sliding modes with nonmatching disturbances.' IEEE Trans. Automat. Contr .. vol. AC-44, 2214-2218, 1999   DOI   ScienceOn
8 H. H. Choi, 'Variable structure control of dynamical systems with mismatched norm-bounded uncertainties:An LMI approach,' Int. J. Control. vol. 74, pp. 1324-1334, 2001   DOI
9 H. H. Choi, 'A new method for variable structure control system design: A linear matrix inequality approach' Automatica, vol. 33, pp. 2089-2092, 1997   DOI   ScienceOn
10 M. Zohdy, M. S. Fadali, and J. Liu, 'Variable structure control using system decomposition,' IEEE Trans. Automat. Contr, vol. AC-37, pp. 1514-1517, 1992   DOI   ScienceOn
11 K.-S. Kim, Y. Park, and S. H. Oh, 'Designing robust sliding hyperplanes for parametric uncertain systems : A Riccati approach,' Automatica, vol. 36, pp. 1041-1048, 2000   DOI   ScienceOn
12 H. H. Choi, 'An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties,' Automatica, vol. 34, pp. 1015-1020, 1998   DOI   ScienceOn
13 H. H. Choi, 'On the existence of linear sliding surfaces for a class of uncertain dynamic systems with mis matched uncertainties,' Automatica, vol. 35, pp. 1707-1715, 1999   DOI   ScienceOn
14 H. H. Choi, 'Variable structure output feedback control design for a class of uncertain dynamic sytems,' Automatica, vol. 38, pp. 335-341, 2002   DOI   ScienceOn
15 R. H. C. Takahashi and P. L. D. Peres, ' $H_{\infty}$ design of switching surfaces for sliding mode control with non-matching disturbances,' In Proc. of the 36th Conference on Decision and Control, pp. 4046-4051, San Diego, USA, Dec. 1997   DOI
16 D. Yue, S. Won, and O. Kwon, 'Note on robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation,' Transaction on Control. Automation and Systems Engineering, vol. 4, pp. 195-198, 2002
17 성재봉, 권성하, 박승규, 정은태 '정합조건을 만족하지 않는 선형시스템에 대한 슬라이딩 모드제어, '제어.자동화.시스템공학논문지, 제7권, 제3호, pp. 193-197, 2001   과학기술학회마을