LMI-based Design of Integral Sliding Mode Controllers for Mismatched Uncertain Systems

비정합 불확실성을 갖는 시스템을 위한 적분 슬라이딩 모드 제어기의 LMI 기반 설계

  • 최한호 (동국대학교 전기공학과)
  • Received : 2010.03.04
  • Accepted : 2010.07.07
  • Published : 2010.08.01


This paper presents an LMI-based method to design an integral sliding mode controller for 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. Using LMIs we derive an existence condition of a sliding surface. And we give a switching feedback control law. Finally, we give a numerical design example in order to show that the proposed method can be better than the existing results.


  1. R.A. DeCarlo, S.H. Zak, and G.P. Mathews, "Variable structure control of nonlinear multivariable systems: A tutorial," IEEE Proceedings, vol. 76, pp. 212-232, 1988
  2. V.I. Utkin, "Variable structure systems with sliding modes," IEEE Trans. Automat. Contr., vol. 22, pp. 212-222, 1977
  3. C. Edwards, A. Akoachere, and S. K. Spurgeon, "Sliding mode output feedback controller design using linear matrix inequalities," IEEE Trans. Automat. Contr., vol. 46, pp. 115-119, 2001.
  4. 최한호, "선형 슬라이딩 평면의 개선된 존재 조건" 제어자동화 시스템 공학회 논문지, 13권, 9호, pp. 851-855, 2007
  5. J. Ackermann and V.I. Utkin, "Sliding mode control design based on Ackermann's formula", IEEE Trans. Automat. Contr., vol. 43, no. 2, pp. 234-237, 1998
  6. H.H. Choi, "LMI-based sliding surface design for integral sliding mode control of mismatched uncertain systems," IEEE Trans. Automat. Contr., vol. 52. no. 4, pp. 736-742, 2007
  7. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in system and Control Theory, Philadelphia, SIAM, 1994.
  8. U. Shaked "An LPD approach to robust $H_2$ and $H_{\infty}$static output-feedback design," IEEE Trans. Automat. Contr., vol. 48, no.5, pp.866-872, 2003
  9. C. Edwards, "A practical method for the design of sliding mode controllers using linear matrix inequalites," Automatica., vol. 40, pp. 1761-1769, 2004
  10. 최한호, "전차수 슬라이딩 모드 관측기를 대체하는 축소차수 관측기의 LMI 기반 설계," 제어로봇시스템학회 논문지, 14권, 3호, pp. 232-235, 2008