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

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

An Improved Existence Condition of Linear Sliding Surfaces

선형 슬라이딩 평면의 개선된 존재 조건

  • 최한호 (동국대학교 전기공학과)
  • Published : 2007.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the problem of designing a linear sliding surface design for a class of uncertain systems with mismatched unstructured uncertainties. The uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as in the input matrix. In terms of linear matrix inequalities (LMIs), we give a sufficient condition for the existence of linear sliding surfaces guaranteeing the asymptotic stability of the sliding mode dynamics. We show that our LMI condition can be less conservative than the existing conditions and our result supplement the existing results. Finally, we give a numerical example showing that our method can be better than the previous results.

Keywords

References

  1. 최한호, '비정합 불확실성을 갖는 선형 시스템을 위한 LMI 기반 슬라이딩 평면 설계법,' 대한전기학회 논문지, 제 55D 권, 제 9 , pp. 409-413, 2006
  2. S. Boyd, L. EI Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, PA:SIAM, 1994
  3. H. H. Choi, 'A new method for variable structure control system design: A linear matrix inequality approach,' Automatica, vol. 33, pp. 2089-2092, 1997 https://doi.org/10.1016/S0005-1098(97)00118-0
  4. R. H. C. Takahashi and P. L. D. Peres, $H_{\Infty}$ design of switching surfaces for sliding modes control with nonmatching disturbances,' In Proc. 36th IEEE Conf Decision Conf., pp. 4046-4051, San Diego, USA, Dec. 1997
  5. 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 https://doi.org/10.1016/S0005-1098(99)00081-3
  6. 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 https://doi.org/10.1080/00207170110061077
  7. V. I. Utkin, 'Variable structure systems with sliding modes,' IEEE Trans. Automat. Contr., vol. 22, pp. 212-222, 1977 https://doi.org/10.1109/TAC.1977.1101446
  8. P. Gahinet, Nemirovski, A. and Laub, A. J., LMI Control Toolbox User's Guide, MA: The MathWorks Inc., 1995
  9. B. D. O. Anderson, J. B. Moore, Optimal Control:Linear Quadratic Methods, NJ: Prentice Hall, 1989
  10. R. H. C. Takahashi and P. L. D. Peres, $H_{\Infty}$ design of switching surfaces for sliding mode control with non-matching disturbances,' IEE Proc. Contr. Theor. Appl., vol. 145, 435-441, 1998
  11. 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. 44, pp. 2214-2218, 1999 https://doi.org/10.1109/9.802948